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On the zeros of derivatives of Bessel functions Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2024-03-09 Dimitris A. Frantzis, Chrysi G. Kokologiannaki, Eugenia N. Petropoulou
The positive zeros of Jν‴(x) and Jν(n+1)(x) are studied by using classical analysis and the properties of Jν(x). It is proved that Jν‴(x) has a unique zero in specific intervals. Regarding Jν(n+1)(...
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New results on the associated Meixner, Charlier, and Krawtchouk polynomials Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2024-03-06 Khalid Ahbli
We give new explicit formulas as well as new generating functions for the associated Meixner, Charlier, and Krawtchouk polynomials. The obtained results are then used to derive new generating funct...
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Approaching the Riemann hypothesis using Salem's equivalence and inversion formulae of a Widder–Lambert-type transform Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2024-02-27 B. J. González, E. R. Negrín
In this paper, we obtain a Post-Widder-type inversion formula for a Widder–Lambert-type integral transform. We also obtain an Lp inversion formula, 1
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Linear canonical Fourier–Bessel wavelet transform: properties and inequalities Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2024-02-21 H. B. Mohamed, A. Saoudi
The purpose of this paper is to introduce and study the linear canonical Fourier–Bessel wavelet transform. We prove an orthogonality relation, inversion formula and some inequality for linear canon...
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On a higher-order version of a formula due to Ramanujan Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2024-02-01 J. M. Campbell
A special case of an Entry in Part II of Ramanujan's Notebooks is such that 1+15(12)2+19(1⋅32⋅4)2+⋯=Γ4(14)16π2. This formula leads us to consider the higher-order version of the above series given...
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Uniqueness and stability for a seismic-type generalized Radon transform Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2024-01-30 Rim Gouia-Zarrad, Sunghwan Moon
In this paper, we consider a generalized seismic Radon transform that maps a given function to its integrals over a certain family of curves in the plane. Such transforms arise in many areas of mat...
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Finite transforms with applications to Bessel differential equations of order higher than two Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2024-01-30 Gabriel López Garza
A finite transformation method is introduced. This method is equivalent to the Z transform method to a certain extent but generalizes it. By applying the presented method to the Bessel functions, i...
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On the fractional space-time Fourier transforms Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2024-01-30 Youssef El Haoui, Mohra Zayed
The notion of a fractional space-time Fourier transform (FSFT) is outlined in this paper, and the properties of invertibility, linearity, Plancherel and others are derived. By establishing the rela...
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Fractional Stockwell transform of Lizorkin distributions Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2024-01-30 Snježana Maksimović
We prove the continuity of the fractional Stockwell transform and the corresponding synthesis operator on the spaces of highly localized functions over R and R×R∖{0}, respectively, and their dual...
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Operational rules for a new family of d-orthogonal polynomials of Laguerre type Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2024-01-30 Wissem Benamira, Ahmed Nasri, Fateh Ellaggoune
The aim of this research is to present a new generalization of d-orthogonal (d≥2) polynomials of Laguerre type by utilizing a suitable generating function from Sheffer class and employing operatio...
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inequality for a modified Struve transform Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2024-01-30 Selma Negzaoui, Nesrin Yousfi
In this paper, we aim to establish an L2 inequality for a Modified Struve transform of order α, denoted as Sα. For this purpose, we use Titchmarsh's method consisting of applying Mellin transform...
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On the Big Hartley transform Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2024-01-30 Fethi Bouzeffour, Wissem Jedidi
In this paper, we introduce a new type of singular first-order differential-difference operator of Dunkl type on the real line. This operator is obtained as a limiting case from both the first-orde...
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Several characterizations of third-degree semiclassical linear forms of class two appearing via cubic decomposition Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2024-01-19 Mohamed Khalfallah
In this work, we consider orthogonal polynomials via cubic decomposition in the framework of the third-degree semiclassical class. Based on their third-degree character, we give a complete descript...
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Fractional Riesz–Feller type derivative for the one dimensional Dunkl operator and Lipschitz condition Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2024-01-03 Fethi Bouzeffour, Wissem Jedidi
In this paper, utilizing the Dunkl transform and a generalized translation operator, we derive an analogue of the Riesz-Feller fractional derivative for a class of functions satisfying Lipschitz co...
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Positivity of oscillatory integrals and Hankel transforms Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2024-01-03 Yong-Kum Cho, Seok-Young Chung, Young Woong Park
In consideration of the integral transform whose kernel arises as an oscillatory solution of certain second-order linear differential equation, its positivity is investigated on the basis of Sturm'...
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On connection between zeros and d-orthogonality Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2024-01-03 Neila Ben Romdhane, Hana Boukattaya
Connection between the interlacing of the zeros and the orthogonality of a given sequence of polynomials is done by K. Driver. In this paper, we attempt to extend this result to some particular cas...
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Generalization of the Ramanujan's integrals for the Volterra μ-functions via complex contours: representations and approximations Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2024-01-03 Arman Hashemzadeh Kalvari, Alireza Ansari, Hassan Askari
In this paper, we consider the inverse Laplace transform of the Volterra μ-function (the Bromwich integral) and evaluate it with respect to the Hankel, Schläfli and Bourguet complex contours. In th...
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Boas-type results for Mellin transform Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2023-12-13 S. S. Volosivets
In this paper, we give necessary and sufficient conditions for a continuous on R+ function f to belong the symmetric generalized Lipschitz classes defined by the Mellin translation in terms of gro...
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A response letter for the editor's reports on the paper: On the polyconvolution operator with a trigonometric weight function for Hartley integral transforms and applications Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2023-12-13 Nguyen Minh Khoa
Published in Integral Transforms and Special Functions (Vol. 35, No. 3, 2024)
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Inversion of Bessel potentials associated with the Dunkl operators on IRd Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2023-12-13 Samir Kallel
The inversion of Bessel potentials is given by using a special-type weighted wavelet transform in the context of Dunkl harmonic analysis on IRd. It has also proved the Calderón-type reproducing fo...
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Mellin transform of shifted Airy functions and of their products Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2023-12-13 E. G. Abramochkin
The Mellin transforms of some products of two shifted Airy functions are evaluated in a closed form. The relation between the Mellin transforms of a single Airy function and the square of the funct...
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Abelian and Tauberian results for the fractional Fourier and short-time Fourier transforms of distributions Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2023-09-06 Sanja Atanasova, Snježana Maksimović, Stevan Pilipović
We introduce the fractional short-time Fourier transform in S′(R) and provide generalized asymptotics for the fractional Fourier and the short-time Fourier transforms within S′(R). Abelian- and T...
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Sufficient conditions for the weighted integrability of Fourier–Laguerre transforms Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2023-08-30 Othman Tyr, Radouan Daher
The problem of weighted integrability of the Fourier–Laguerre transform in terms of the moduli of smoothness related to generalized translations is considered. Sufficient conditions are given to so...
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On some relations in the class of multi-index Mittag-Leffler functions Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2023-08-18 Jordanka Paneva-Konovska, Sarah A. Deif
In this paper, some properties related to the 3m-parametric Mittag-Leffler (M-L) functions are investigated. More precisely, three families of such functions with different kinds of indices are ex...
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Binomial identities obtained from the Gegenbauer series expansion Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2023-08-11 Omran Kouba
Using the Fourier–Gegenbauer series, we prove several identities that generalize known results. In particular, it is proved, that ∑n=0∞14n(2nn)z−2n(z−1/2n)(zn)3=tan(πz)π for all complex numbers ...
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Properties of the fractional Clifford–Fourier transform Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2023-08-09 Haipan Shi, Heju Yang, Yuying Qiao
In this paper, we establish a Riemann–Lebesgue theorem and some real Paley–Wiener-type theorems for the fractional Clifford–Fourier transform (FrCFT). Furthermore, because of the non-commutativity ...
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On some formulas for the confluent Horn functions H10(c) (a; c; w, z) and H11(c) (a, c, c′; d; w, z) Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2023-08-07 Yu A. Brychkov, N. V. Savischenko
Some new relations for the confluent Horn functions H10(c)(a;c;w,z) and H11(c)(a,c,c′;d;w,z) are obtained including differentiation and integration formulas, series and reduction formulas. Some g...
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On the Barnes double gamma function Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2023-07-21 S. Alexanian, A. Kuznetsov
We aim to achieve the following three goals. First of all, we collect all known definitions, transformation properties and functional identities of Barnes double gamma function G(z;τ). Second, we ...
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New series expansions for the ℋ-function of communication theory Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2023-07-11 Chelo Ferreira, José L. López, Ester Pérez Sinusía
The H-function of communication theory plays an important role in the error rate analysis in digital communication with the presence of additive white Gaussian noise (AWGN) and generalized multipa...
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On the polyconvolution operator with a trigonometric weight function for the Hartley integral transforms and applications Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2023-07-03 Nguyen Minh Khoa
The main aim of this work is to establish a new polyconvolution operator with the weight function γ=siny for the Hartley integral transforms. After that, we will apply it to solve some classes of...
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Product formula for the one-dimensional (k,a)-generalized Fourier kernel Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2023-06-08 Béchir Amri
In this paper, a product formula for the one-dimensional (k,a)-generalized Fourier kernel is given for k≥0, a>0 and 2k>1−a2, extending the special case of [Boubatra MA, Negzaoui S, Sifi M. A new...
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Generalized translation and convolution associated to the linear canonical Fourier–Jacobi transform Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2023-05-22 Abdellatif Akhlidj, Fatima Elgadiri, Afaf Dahani
In this paper, we introduce the Canonical Fourier-Jacobi transform, which is a generalization of Fractional Fourier-Bessel transform. We define and study the translation operator and we also derive...
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Constructing basises in solution space of the system of equations for the Lauricella Function FD(N) Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2023-05-17 S. I. Bezrodnykh
The paper considers the issue of constructing basises in the solution space of the system of partial differential equations, which is satisfied by the Lauricella hypergeometric function FD(N)(a;b,...
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Iteration of the Laplace transform over generalized functions and a Post-Widder inversion formula over distributions of compact support Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2023-05-14 B. J. González, E. R. Negrín
In this paper, we deal with the iteration of the Laplace transform over certain spaces of generalized functions. As a consequence we prove a new Post-Widder-type inversion formula for this transfor...
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Calderón's reproducing formulas for the poly-axially Lα2-multiplier operators Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2023-03-22 Belgacem Selmi, Rahma Chbeb
We study the poly-axially Lα2-multiplier operators on IR+n and we give for them some Calderón's reproducing formulas and best approximation using the theory of reproducing kernels.
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Upper bounds and asymptotic expansion for Macdonald's function and the summability of the Kontorovich-Lebedev integrals Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2023-03-21 S. Yakubovich
Uniform upper bounds and the asymptotic expansion with an explicit remainder term are established for the Macdonald function Kiτ(x)Kiτ(x) . The results can be applied, for instance, to study the summability of the divergent Kontorovich-Lebedev integrals in the sense of Jones. Namely, we answer affirmatively a question (cf. [Ehrenmark U. Summability experiments with a class of divergent inverse Kontorovich-Lebedev
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On some relations between hyper Bessel–Clifford, Macdonald and Meijer functions and hyper Hankel–Clifford integral transforms Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2023-03-21 I. A. Shilin, Junesang Choi
Using a representation of the unimodular Lorentz group, we derive some relations between hyper Bessel–Clifford, Macdonald and Meijer functions. We obtained them as two additional theorems (continual and countable) for a functional defined on the above group and a pair of basis functions belonging to representation spaces. Introducing a hyper analogue of the known first and second Hankel–Clifford integral
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The indefinite integrals of Meijer's G-functions from integrating factors Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2023-03-16 A. Saboor, Arshid Khan, Nisar Ahmad
Conway [A Lagrangian method for deriving new indefinite integrals of special functions. Integral Transforms Spec Funct. 2015;26:812–824] introduced a new and simple method named the ‘Lagrangian method’ for deriving indefinite integrals of both elementary and special functions, provided the function satisfies the second-order linear differential equation. In this paper, different Meijer's G-functions
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On the quasi-orthogonality and Hahn-classical d-orthogonal polynomials Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2023-03-08 Abdessadek Saib
This paper focuses on the quasi-orthogonality between sequences of d-orthogonal polynomials and their characterization in terms of linear combinations as well as the left product of vector of linear forms by matrix polynomial. Therefore, structure relations for Hahn-classical d-orthogonal polynomials are provided.
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On convergence of Fourier series in discrete Jacobi–Sobolev spaces Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2023-03-07 Ó. Ciaurri, J. Mínguez Ceniceros, J. M. Rodríguez
In this paper, we show a complete characterization of the uniform boundedness of the partial sum operator in a discrete Sobolev space with Jacobi measure. As a consequence, we obtain the convergence of the Fourier series. Moreover it is showed that this Sobolev space is the first category which implies that it is not possible to apply the Banach–Steinhaus theorem.
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Young inequalities for a Fourier cosine and sine polyconvolution and a generalized convolution Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2023-03-06 Trinh Tuan, Vu Kim Tuan
In this paper, we obtain some Young type inequalities for a polyconvolution and a generalized convolution involving the Fourier-cosine and Fourier-sine integral transforms.
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Two-dimensional contiguous relations for the linearization coefficients of classical orthogonal polynomials Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2023-03-01 Howard S. Cohl, Lisa Ritter
ABSTRACT By using the three-term recurrence relation for orthogonal polynomials, we produce a collection of two-dimensional contiguous relations for certain generalized hypergeometric functions. These generalized hypergeometric functions arise through linearization coefficients for some classical orthogonal polynomials in the Askey-scheme, namely Gegenbauer (ultraspherical), Hermite, Jacobi and Laguerre
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Characterization of orthogonal polynomials on lattices Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2023-03-01 D. Mbouna, Juan F. Mañas–Mañas, Juan J. Moreno–Balcázar
We consider two sequences of orthogonal polynomials (Pn)n≥0(Pn)n≥0 and (Qn)n≥0(Qn)n≥0 such that ∑Mj=1aj,nSxDkxPk+n−j(z)=∑Nj=1bj,nDmxQm+n−j(z), with k,m,M,N∈N, aj,n and bj,n are sequences of complex numbers, 2Sxf(x(s))=(△+2I)f(z),Dxf(x(s))=△△x(s−1/2)f(z), z=x(s−1/2), I is the identity operator, x defines a lattice, and △f(s)=f(s+1)−f(s). We show that under some natural conditions, both involved orthogonal
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Identities for combinatorial sums involving trigonometric functions Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2023-02-21 H. Alzer, S. Yakubovich
Let Am,n(a)=∑mj=0(−4)j(m+j2j)∑n−1k=0sin(a+2kπ/n)cos2j(a+2kπ/n)Am,n(a)=∑j=0m(−4)j(m+j2j)∑k=0n−1sin(a+2kπ/n)cos2j(a+2kπ/n) and Bm,n(a)=∑j=0m(−4)j(m+j+12j+1)∑k=0n−1sin(a+2kπ/n)×cos2j+1(a+2kπ/n),Bm,n(a)=∑j=0m(−4)j(m+j+12j+1)∑k=0n−1sin(a+2kπ/n)×cos2j+1(a+2kπ/n), where m≥ 0m≥ 0 and n≥ 1 are integers and a is a real number. We present two proofs for the following results: If 2m+1≡0(modn), then Am,n(a
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Kontorovich–Lebedev wavelet transform on Besov type spaces Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2023-02-20 Ashish Pathak, Shrish Pandey
In the present paper, we define Besov type spaces associated with the Kontorovich–Lebedev transform. We widen the concept of continuous Kontorovich–Lebedev wavelet transform on Lp(R+;x−1dx)Lp(R+;x−1dx) space and derive continuity of Kontorovich–Lebedev wavelet transform on Besov type spaces and lastly characterize the Besov Kontorovich–Lebedev space by using Kontorovich–Lebedev wavelet coefficients
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Inversion formula and uncertainty inequalities for the Weinstein-type Segal–Bargmann transform Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2023-02-13 Fethi Soltani, Hanen Saadi
In 1961, Bargmann introduced the classical Segal–Bargmann transform and in 1984, Cholewinsky introduced the generalized Segal–Bargmann transform. These two transforms are the aim of many works, and have many applications in mathematics. In this paper, we introduce the Weinstein-type Segal–Bargmann transform BαBα ; and we prove for this transform Plancherel and inversion formulas. Next, we give a relation
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On the closed form of Clausen functions Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2023-02-04 Slobodan B. Tričković, Miomir S. Stanković
We derive explicit closed-form formulas for the standard Clausen functions Cl2m(x) and Cl2m−1(x) in terms of the Hurwitz zeta function, where m is a positive integer.
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Inversion formulae for a Lambert-type transform and the Salem's equivalence to the Riemann hypothesis Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2023-01-24 B. J. González, E. R. Negrín
In this paper, by means of the classical inversion formula of the Mellin transform and also by means of a L2 inversion formula, we obtain corresponding inversion formulae for a Lambert-type integral transform. As a consequence of these results, we consider some class of functions regarding Salem's equivalence to the Riemann hypothesis.
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The continuous fractional Bessel wavelet transform and its applications Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2023-01-11 S. K. Upadhyay, Kush Kumar Mishra
In this paper, the fractional Bessel wavelet transform is introduced by exploiting the theory of the fractional Hankel transform and the boundedness of the fractional Bessel wavelet transform obtained. Time invariant linear filter associated with the fractional Hankel transform is investigated and its various properties are obtained. In the present paper, authors also expressed time-invariant linear
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Shannon, Sobolev and uncertainty inequalities for the Weinstein transform Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2023-01-10 Néjib Ben Salem
ABSTRACT The objective of this paper is to extend some weighted inequalities for the Weinstein transform. Especially, we are interesting in the study of the Beckner logarithmic inequality, the Shannon inequality. We give a sharp version of this inequality. Next, we establish different Sobolev type embedding theorems in our context. Finally, we deal with some uncertainty inequalities and a logarithmic
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The algebra of difference operators associated to Meixner type polynomials Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2022-12-29 Antonio J. Durán, Mónica Rueda
Meixner type polynomials (qn)n≥0 are defined from the Meixner polynomials by using Casoratian determinants whose entries belong to two given finite sets of polynomials (Sh)h=1m1 and (Tg)g=1m2. They are eigenfunctions of higher-order difference operators but only for a careful choice of the polynomials (Sh)h=1m1 and (Tg)g=1m2, the sequence (qn)n≥0 is orthogonal with respect to a measure. Under mild
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Characterization of the D-Laguerre–Hahn orthogonal polynomials of class one via the cubic decomposition Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2022-12-26 L. Khériji, K. Omrani
In the present work, we deal with a monic orthogonal polynomial sequence (MOPS) deduced by its cubic decomposition (CD) W3n(x)=Pn(x3), n≥0. Our goal is to determine all D-Laguerre–Hahn strict of class one of these sequences. From the CD structure, only one family of MOPS appears in connection with the D-Laguerre–Hahn of class zero of Jacobi type in the singular case and the nonsingular one. Their recurrence
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Quantitative uncertainty principles for the Gabor spherical mean transform Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2022-12-24 Chirine Chettaoui, Amina Hassini, Khalifa Trimèche
In this paper, we present the basic Gabor spherical mean theory. Next, we prove several uncertainty principles for this transform such as Heisenberg type inequalities, Donoho-Stark's uncertaintly principle, Shannon's uncertainty principle, Lp-Heisenberg uncertainty principle and Lp-local uncertainty principles.
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On Neumann series of Macdonald functions Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2022-12-24 Tibor K. Pogány, Najib Laraqi
The main aim of this article is to establish a closed-form expression for the Neumann series built with Macdonald functions in which order contains the summation index and the coefficients include the summation index exponentially and factorially. Motivated by this problem which occurs in several problems of physics or electrochemistry such as diffusion phenomena, we derive two integral representations
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On polynomial transformations preserving purely imaginary zeros* Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2022-12-22 J. L. Hindmarsh, M. C. Lettington
ABSTRACT In this present work polynomial transformations are identified that preserve the property of the polynomials having all zeros lying on the imaginary axis. Existence results concerning families of polynomials whose generalized Mellin transforms have zeros all lying on the critical line ℜs=12 are then derived. Inherent structures are identified from which a simple proof relating to the Gegenbauer
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Sharp weighted Hölder mean bounds for the complete elliptic integral of the second kind Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2022-12-15 Miao-Kun Wang, Zai-Yin He, Tie-Hong Zhao, Qi Bao
ABSTRACT This paper deals with the complete integral of the second kind E(r) approximated by the weighted Hölder mean. In general, there are two ways to be considered. One is to find the best exponential parameters with a given weight, and the other is to find the optimal weights with a given exponential order. The second method will be used in this paper where we find the sharp weighted Hölder mean
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Limits of some integrals connected with Bessel analysis Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2022-12-05 S. S. Platonov
In various sections of the classical Fourier Analysis, the problem of the convergence of the integrals ∫0∞f(λt)g(t)dtas λ→+0 and λ→+∞ under various assumptions on the functions f and g are considered. In this paper, we study some analogues of such problems for weight integrals of the form ∫0∞f(λt)g(t)t2α+1dt,α>−1/2,for functions f and g from some weighted functional classes that are connected with
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Bicomplex hypergeometric function and its properties Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2022-11-30 Rekha Meena, Ajit Kumar Bhabor
The aim of this article is to define the bicomplex hypergeometric function. We obtain some useful results from the theory of special functions over a relatively large domain. We discuss the bicomplex holomorphicity of the bicomplex hypergeometric function and establish some significant relations based on it along with some bicomplex geometric representations of conditions of existence.
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Contiguous values for a class of nonterminating 3F2(1)-series Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2022-11-30 Marta Na Chen, Wenchang Chu
By employing the linearization method and partial fractions, we examine a large class of nonterminating exotic 3F2-series extended by five integer parameters. A general summation formula is proved, and several contiguous series are evaluated in closed form.
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The h-Fourier sine-Laplace discrete generalized convolution on time scale Integral Transform. Spec. Funct. (IF 1.0) Pub Date : 2022-11-10 Hoang Tung, Nguyen Xuan Thao, Vu Kim Tuan
In this paper, we introduce h-Fourier sine-Laplace discrete generalized convolution. We study a class of generalized convolution transforms and give necessary and sufficient conditions so that the transformations are unitary. As application, we obtain solutions in explicit form of some classes of the Toeplitz plus Hankel-type equations related to the h-Fourier sine-Laplace generalized convolution.