In this paper, we study the recurrence coefficients of a deformed Hermite polynomials orthogonal with respect to the weight w(x;t,α):=e−x2|x−t|α(A+B⋅𝜃(x−t)),x∈(−∞,∞), where α>−1,A≥0,A+B≥0 and t∈ℝ. It is an extension of Chen and Feigin [J. Phys. A., Math. Gen. 39 (2006) 12381–12393]. By using the ladder operator technique, we show that the recurrence coefficients satisfy a particular Painlevé IV equation

We study the limiting distribution of a pair counting statistics of the form ∑1≤i≠j≤Nf(LN(𝜃i−𝜃j)) for the circular β-ensemble (CβE) of random matrices for sufficiently smooth test function f and LN=O(N). For β=2 and LN=N our results are inspired by a classical result of Montgomery on pair correlation of zeros of Riemann zeta function.

Subordination is the basis of the analytic approach to free additive and multiplicative convolution. We extend this approach to a more general setting and prove that the conditional expectation 𝔼φ(z−X−f(X)Yf∗(X))−1|X for free random variables X,Y and a Borel function f is a resolvent again. This result allows the explicit calculation of the distribution of noncommutative polynomials of the form X+f(X)Yf∗(X)

Professional forecasters can rely on econometric models, on their personal expertise or on both. To accommodate for adjustments to model forecasts, this paper proposes to use Two Stage Least Squares (and not Ordinary Least Squares) for the familiar Mincer‐Zarnowitz regression when examining bias in professional forecasts, where the instrumental variable is the consensus forecast. An illustration for

This paper shows that shocks to the equity capital ratio of financial intermediaries (CRFI) have predictive ability for stock realized volatility, from both in‐sample and out‐of‐sample perspectives. The revealed predictability is also of economic significance, in that it examines the performance of portfolios constructed on the basis of CRFI forecasts of stock volatility. Robustness test results suggest

We study the space BMO𝒢 (𝕏) in the general setting of a measure space 𝕏 with a fixed collection 𝒢 of measurable sets of positive and finite measure, consisting of functions of bounded mean oscillation on sets in 𝒢. The aim is to see how much of the familiar BMO machinery holds when metric notions have been replaced by measure-theoretic ones. In particular, three aspects of BMO are considered:

In the present paper, we introduce a family of the approximating problems corresponding to an elliptic obstacle problem with a double phase phenomena and a multivalued reaction convection term. Denoting by 𝓢 the solution set of the obstacle problem and by 𝓢n the solution sets of approximating problems, we prove the following convergence relation

Nonlinear parabolic equations are frequently encountered in applications and efficient approximating techniques for their solution are of great importance. In order to provide an effective scheme for the temporal approximation of such equations, we present a sum splitting scheme that comes with a straightforward parallelization strategy. The convergence analysis is carried out in a variational framework

We introduce a Markov product structure for multivariate tail dependence functions, building upon the well-known Markov product for copulas. We investigate algebraic and monotonicity properties of this new product as well as its role in describing the tail behaviour of the Markov product of copulas. For the bivariate case, we show additional smoothing properties and derive a characterization of idempotents

When a function belonging to a fractional-order Sobolev space is supported in a proper subset of the Lipschitz domain on which the Sobolev space is defined, how is its Sobolev norm as a function on the smaller set compared to its norm on the whole domain? On what do the comparison constants depend on? Do different norms behave differently? This article addresses these issues. We prove some inequalities

Let A be the UHF-algebra of 2∞-type, B be a non-unital but σ-unital stably finite simple C⁎-algebra with real rank zero and a continuous scale. In this paper, we give a classification of the following essential extensions of A by B⊗A:0→B⊗A→E→A→0, up to unitary equivalence. Denote by Ext(A,B⊗A), the abelian group of unitary equivalence classes of essential extensions of A by B⊗A. There is a group isomorphismΓ:Ext(A

The concepts of differentiation and integration for matrices were introduced for studying zeros and critical points of complex polynomials. Any matrix is differentiable, however not all matrices are integrable. The purpose of this paper is to investigate the integrability property and characterize it within the class of diagonalizable matrices. In order to do this we study the relation between the

In this paper, we study the curvature estimates of the conformal Ricci flow on Riemannian manifolds. We show that the norm of the Weyl tensors of any smooth solution to the conformal Ricci flow can be explicitly estimated in terms of its initial values on a given ball, a local uniform bound on the Ricci tensors, and the potential function. On the compact manifold, the curvature operator remains bounded

In this paper, we investigate the existence of global classical solution to the Cauchy problem for the three-dimensional micropolar fluid equations with vacuum. Precisely, when the far-field density is vacuum, we get the global classical solution under the assumption that (γ−1)13E0 is suitably small, where γ is the adiabatic exponent and E0 is the initial energy. This is a Nishida-Smoller type global

We consider minimizers of the functional∫Ωf(x,u,Du)dx, where f is asymptotically related the function (x,u,ξ)↦a(x,u)G(ξ), with G a function with p-Uhlenbeck structure and a∈C0(Ω×RN). The main contribution of this article is to refine the growth estimate imposed on f. In particular, we assume that|f(x,u,ξ)|≤μ1(x)+μ2(x)|u|s+M(1+|ξ|2)p2, where μ2∈Lγ,β(Ω) for some numbers β and γ. By assuming only that

Let M be a von Neumann algebra, and let 0

We study the existence of positive solutions for a semi-linear elliptic equation involving both critical growth and singular nonlinearity. By applying the Nehari manifold and Lusternik-Schnirelmann category theory to an auxiliary problem, we prove the existence of multiple positive solutions.

We introduce and investigate the Teichmüller space T0Z of diffeomorphisms of the unit circle with Zygmund continuous derivatives. We first give some characterizations of such diffeomorphism by means of the complex dilatation of its quasiconformal extension and the logarithmic and Schwarzian derivatives of its normalization decomposition. Also, we characterize the quasicircle which corresponds to circle

In this paper, we consider the existence of solutions for the quasilinear elliptic problem:(P1){−div(A(x,u)∇u)+12At(x,u)|∇u|2=g(x,u)+h(x),inΩ,u=0,on∂Ω, where Ω⊂RN is a open bounded domain, N≥3, the real term A(x,t), At(x,t)=∂A∂t(x,t) and g(x,t) satisfy Carathéodory condition on Ω×R and h:Ω→R is a given measurable function. The intention of the article is to get new results of the existence of infinitely

Let X be a non-compact symmetric space of dimension n. We prove that if f∈Lp(X), 1≤p≤2, then the Riesz means SRz(f) converge to f almost everywhere as R→∞, whenever Rez>(n−12)(2p−1).

We consider an incompressible and inviscid conducting fluid in the presence of surface tension and vertical electric field. We will reduce the system to the equations on the interface and the velocity fields. By the reduced equations, it is obtained the local-in-time estimates on the interface in H3k+1 and the velocity fields in H3k by using the method introduced by Shatah and Zeng [20]. The estimates

In this paper we establish the local regularity estimates in Besov spaces of weak solutions for the elliptic p(x)-Laplacian equation with the logarithmic growth in divergence formdiv(|∇u|p(x)−2ln⁡(e+|∇u|)∇u)=divF under some proper assumptions on the functions p(x) and F. Moreover, it is worth noting that our results improve the known results for these types of equations.

In this paper we establish mapping properties of bilinear Coifman-Meyer multipliers acting on the product spaces H1(Rn)×bmo(Rn) and Lp(Rn)×bmo(Rn), with 1

We prove an analogue of a perturbation result for the Dirichlet problem of divergence form elliptic operators by Fefferman, Kenig and Pipher, for the degenerate elliptic operators of David, Feneuil and Mayboroda, which were developed to study geometric and analytic properties of sets with boundaries whose co-dimension is higher than 1. These operators are of the form −divA∇, where A is a weighted elliptic

We derive rigorously the 2D periodic focusing cubic NLS as the mean-field limit of the 3D focusing quantum many-body dynamics describing a dilute Bose gas with periodic boundary condition in the x-direction and a well of infinite-depth in the z-direction. Physical experiments for these systems are scarce. We find that, to fulfill the empirical requirement for observing NLS dynamics in experiments,

We provide the rigorous foundations for a categorical approach to the classification of C⁎-dynamics up to cocycle conjugacy. Given a locally compact group G, we consider a category of (twisted) G-C⁎-algebras, where morphisms between two objects are allowed to be equivariant maps or exterior equivalences, which leads to the concept of so-called cocycle morphisms. An isomorphism in this category is precisely

A priori estimates for semilinear higher order elliptic equations usually have to deal with the absence of a maximum principle. This note presents some regularity estimates for the polyharmonic Dirichlet problem that will make a distinction between the influence on the solution of the positive and the negative part of the right-hand side.

Modulation spaces Mp,qs were introduced by Feichtinger [11] in 1983. Bényi and Oh [2] defined a modified version to Feichtinger's modulation spaces for which the symmetry scalings are emphasized for its possible applications in PDE. By carefully investigating the scaling properties of modulation spaces and their connections with Bényi and Oh's modulation spaces, we introduce the scaling limit versions

In this paper, we study continuous frames from projective representations of locally compact abelian groups of type \(\widehat{G}\times G\). In particular, using the Fourier transform on locally compact abelian groups, we obtain a characterization of maximal spanning vectors. As an application, for G, a compactly generated locally Euclidean locally compact abelian group or a local field with odd residue

Reconstruction of signals by their Fourier (transform) samples is investigated in many mathematical/engineering problems such as the inverse Radon transform and optical diffraction tomography. This paper concerns on the reconstruction of spline-spectra signals in \(V(\hbox {sinc}_{a})\) by finitely many Fourier samples, where \(\hbox {sinc}_{a}\) is the generalized sinc function. There are two main

For certain families of compact subsets of the plane, the isomorphism class of the algebra of absolutely continuous functions on a set is completely determined by the homeomorphism class of the set. This is analogous to the Gelfand–Kolmogorov theorem for C(K) spaces. In this paper, we define a family of compact sets comprising finite unions of convex curves and show that this family has the ‘Gelfand–Kolmogorov’

We obtain bounds for the numerical radius of \(2 \times 2\) operator matrices which improve on the existing bounds. We also show that the inequalities obtained here generalize the existing ones. As an application of the results obtained here, we estimate the bounds for the zeros of a monic polynomial and illustrate with numerical examples that the bounds are better than the existing ones.

In this paper we study stability issues for vectorial directional minima of sets and set-valued constrained optimization problems. In our work we consider several constructions and tools from interiority properties, enlargement of cones and the extremal principle to generalized Lipschitz properties. Our results complete the literature in this area of research, by proposing a different set of hypotheses

This paper uses relative symplectic cohomology, recently studied by Varolgunes, to understand rigidity phenomena for compact subsets of symplectic manifolds. As an application, we consider a symplectic crossings divisor in a Calabi–Yau symplectic manifold M whose complement is a Liouville manifold. We show that, for a carefully chosen Liouville structure, the skeleton as a subset of M exhibits strong

Inspired by an extension of Wiener's lemma on the relation of measures μ on the unit circle and their Fourier coefficients μˆ(kn) along subsequences (kn) of the natural numbers by Cuny, Eisner and Farkas [1], we study the validity of the lemma when the Fourier coefficients are weighted by a sequence of probability measures. By using convergence with respect to a filter derived from these measure sequences

In this paper, we study the basic Riemann-Hilbert (RH) problem of the coupled dispersive AB system with the Schwartz class of initial value problems starting from the Lax pair. We use the Deift-Zhou nonlinear steepest-descent method to analyze the obtained RH problem such that the long-time asymptotics of the solutions of this coupled AB system is found as t→∞.

We show that the gluing construction for Hilbert modules introduced by Raeburn in his computation of the Picard group of a continuous-trace C⁎-algebra (Trans. Amer. Math. Soc., 1981) can be applied to arbitrary C⁎-algebras, via an algebraic argument with the Haagerup tensor product. We put this result into the context of descent theory by identifying categories of gluing data for Hilbert modules over

In this work, we provide a characterization result for lower semicontinuity of surface energies defined on piecewise rigid functions, i.e., functions which are piecewise affine on a Caccioppoli partition where the derivative in each component is a skew symmetric matrix. This characterization is achieved by means of an integral condition, called BD-ellipticity, which is in the spirit of BV-ellipticity

One proves the existence and uniqueness of a generalized (mild) solution for the nonlinear Fokker–Planck equation (FPE)ut−Δ(β(u))+div(D(x)b(u)u)=0,t≥0,x∈Rd,d≠2,u(0,⋅)=u0,in Rd, where u0∈L1(Rd), β∈C2(R) is a nondecreasing function, b∈C1, bounded, b≥0, D∈(L2∩L∞)(Rd;Rd) with divD∈L∞(Rd), and divD≥0, β strictly increasing, if b is not constant. Moreover, t→u(t,u0) is a semigroup of contractions in L1(Rd)

This paper deals with the 1/κα-type area-preserving nonlocal flow of smooth convex closed plane curves for all constant α>0. Under this flow, the convexity of the evolving curve is preserved. Due to the existence of finite time curvature blow-up examples, it is shown that, if the curvature κ will not blow up in finite time, the evolving curve will converge smoothly to a circle as t→∞.

The natural BMO (bounded mean oscillation) conditions suggested by scalar-valued results are known to be insufficient for the boundedness of operator-valued paraproducts. Accordingly, the boundedness of operator-valued singular integrals has only been available under versions of the classical “T(1)∈BMO” assumptions that are not easily checkable. Recently, Hong, Liu and Mei (J. Funct. Anal. 2020) observed

Dunkl operators associated with finite reflection groups generate a commutative algebra of differential-difference operators. There exists a unique linear operator called intertwining operator which intertwines between this algebra and the algebra of standard differential operators. There also exists a generalization of the Fourier transform in this context called Dunkl transform. In this paper, we

In the theory of 2D Ginzburg-Landau vortices, the Jacobian plays a crucial role for the detection of topological singularities. We introduce a related distributional quantity, called the global Jacobian that can detect both interior and boundary vortices for a 2D map u. We point out several features of the global Jacobian, in particular, we prove an important stability property. This property allows

In this paper, we provide a new reformulation of the quadratic analogue of the Weyl relations. Especially, we offer some adjustments [10] on these relations and the corresponding group law, i.e., the quadratic Heisenberg group law. We provide a much more transparent description of the underlying manifold and we give a connection with the projective group PSU(1,1). Finally, we deduce such a holomorphic

In this paper, with the help of a variant of Schauder fixed point theorem in the real Banach algebra together with the finite difference method (FDM), we take a brief look at the p-adic analog of Richards’ equation derived by Khrennikov et al. [Application of p-adic wavelets to model reaction–diffusion dynamics in random porous media, J. Fourier Anal. Appl.22 (2016) 809–822], and study the solvability

In this paper, we establish a Freidlin–Wentzell-type large deviation principle for stochastic models of two-dimensional second grade fluids driven by Lévy noise. The weak convergence method introduced by Budhiraja, Dupuis and Maroulas plays a key role.

Let Φ be a locally convex space and let Φ′ denote its strong dual. In this paper, we introduce sufficient conditions for the existence of a continuous or a càdlàg Φ′-valued version to a cylindrical process defined on Φ′. Our result generalizes many other known results on the literature and their different connections will be discussed. As an application, we provide sufficient conditions for the existence

In this paper, we introduce a new white noise delta function based on the Kubo–Yokoi delta function and an infinite-dimensional Brownian motion. We also give a white noise differential equation induced by the delta function through the Itô formula introducing a differential operator directed by the time derivative of the infinite-dimensional Brownian motion and an extension of the definition of the

We prove a stochastic Gronwall lemma of the convolution type. Our results extend that of Scheutzow [A stochastic Gronwall lemma, Infin. Dimens. Anal. Quantum Probab. Relat. Top.16 (2013) 1350019], and the related results established in the non-convolution case. The proofs of the present results are essentially based on the Métivier–Pellaumail inequality for semimartingales.

This paper examines the recession probability in the Eurozone within the next 12 months at the zero lower bound (ZLB) and explores two new perspectives: a revised measure of the traditional term spread and a modification to detect unstable dynamics driven by animal spirits. We find that the yield curve largely lost its forecasting ability at the ZLB. To remove the downward rigidity of short‐term rates

Magnetic Resonance Imaging (MRI) is one of the most important techniques in medical imaging and Rician noise is a common noise that naturally appears in MRI images. Low rank matrix approximation approaches have been widely used in image processing such as image denoising, which takes advantage of the idea of non-local self-similarity between patches in a natural image. The weighted nuclear norm minimization

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 453-490, January 2021. A discrete-to-continuum analysis for free-boundary problems related to crystalline films deposited on substrates is performed by $\Gamma$-convergence. The discrete model introduced here is characterized by an energy with two contributions, the surface and the elastic-bulk energy, and it is formally justified starting

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 435-452, January 2021. We study a class of fractional parabolic equations involving a time-dependent magnetic potential and formulate the corresponding inverse problem. We determine both the magnetic potential and the electric potential from the exterior partial measurements of the Dirichlet-to-Neumann map.

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 386-434, January 2021. We study the reducibility of a linear Schrodinger equation subject to a small unbounded almost periodic perturbation which is analytic in time and space. Under appropriate assumptions on the smallness, analyticity, and on the frequency of the almost periodic perturbation, we prove that such an equation is reducible

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 351-385, January 2021. We provide explicit examples to show that the relaxation of functionals $L^p(\Omega;{\mathbb{R}}^m) \ni u\mapsto \int_\Omega\int_\Omega W(u(x), u(y))\, dx\, dy$, where $\Omega\subset{\mathbb{R}}^n$ is an open and bounded set, $1

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 323-350, January 2021. We study the global existence and uniform-in-time bounds of classical solutions in all dimensions to reaction-diffusion systems dissipating mass. By utilizing the duality method and the regularization of the heat operator, we show that if the diffusion coefficients are close to each other, or if the diffusion coefficients

We provide a new separation-based proof of the domination theorem for (q, 1)-summing operators. This result gives the celebrated factorization theorem of Pisier for (q, 1)-summing operators acting in C(K)-spaces. As far as we know, none of the known versions of the proof uses the separation argument presented here, which is essentially the same that proves Pietsch Domination Theorem for p-summing operators

This paper is about the well-posedness and stability in set optimization with applications to vector-valued games involving uncertainty. Some characterizations for several types of well-posedness with their relations in set optimization are given under mild conditions. Some sufficient and necessary conditions for these types of well-posedness in set optimization are also given by using the local C-Lipschitz

Assume that X is a reflexive Banach space with an unconditional basis. In this paper, we show that the Banach space K(X) of compact operators on X has Pełczyński’s property V.

In this paper, we introduce a \(C^{0}\) virtual element method for the Helmholtz transmission eigenvalue problem, which is a fourth-order non-selfadjoint eigenvalue problem. We consider the mixed formulation of the eigenvalue problem discretized by the lowest-order virtual elements. This discrete scheme is based on a conforming \(H^{1}(\varOmega )\times H^{1}(\varOmega )\) discrete formulation, which