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  • On Entire Solutions of a Pythagorean Functional Equation and Associated PDEs
    Complex Anal. Oper. Theory (IF 0.711) Pub Date : 2020-05-29
    Bao Qin Li, Feng Lü

    We will show, among other things, that an entire holomorphic map \((f(z_1, z_2), g(z_1, z_2))\) from \(\mathbb {C}^2\) into the simple-looking surface \(x^2+y^2=1\) in \(\mathbb {C}^2\) reduces to constant if and only if \(f^{-1}_{z_2}(0)\subseteq g^{-1}_{z_1}(0)\) (ignoring multiplicities) unless \(g^{-1}_{z_1}(0)={\mathbb {C}}^2\). Applications to nonlinear partial differential equations and certain

    更新日期:2020-05-29
  • Nonlocal Fractional Differential Equations and Applications
    Complex Anal. Oper. Theory (IF 0.711) Pub Date : 2020-05-28
    Veli Shakhmurov

    The regularity properties of nonlocal fractional differential equations in Banach spaces are studied. Uniform \(L_{p}\)-separability properties and sharp resolvent estimates are obtained for abstract elliptic operator in terms of fractional derivatives. Particularly, it is proven that the fractional elliptic operator generated by these equations is sectorial and also is a generator of an analytic semigroup

    更新日期:2020-05-28
  • New Paley–Wiener Theorems
    Complex Anal. Oper. Theory (IF 0.711) Pub Date : 2020-05-27
    Ha Huy Bang, Vu Nhat Huy

    In this paper, for an arbitrary fixed compact set K, we find necessary and sufficient conditions on the Taylor expansion coefficients of entire functions of exponential type so that these functions are the Fourier image of distributions supported in K. In other words, we state the Paley–Wiener theorem in the language of Taylor expansion coefficients.

    更新日期:2020-05-27
  • On Convolution of Harmonic Mappings
    Complex Anal. Oper. Theory (IF 0.711) Pub Date : 2020-05-27
    Subzar Beig

    For \(j=1,2,\) let the sense-preserving locally univalent harmonic mappings \({\mathcal {F}}_j={\mathcal {H}}_j+\overline{{\mathcal {G}}_j}\) on \({\mathcal {D}}:=\left\{ z\in {\mathbb {C}}: |z|<1\right\} \) be such that \(\overline{{\mathcal {F}}_j({\overline{z}})}={\mathcal {F}}_j(z)\) and the mappings \(z({\mathcal {H}}_j+{\mathcal {G}}_j)'\) are either odd starlike or starlike of order 1/2. It

    更新日期:2020-05-27
  • Extension of Besov-Q Type Spaces via Convolution Operators with Applications
    Complex Anal. Oper. Theory (IF 0.711) Pub Date : 2020-05-24
    Fang Han, Pengtao Li

    In this paper, we use regular wavelets to investigate the extension problem of a class of Besov-Q spaces \({\dot{B}}^{\alpha ,\lambda }_{p,p}({\mathbb {R}}^{n})\). We introduce an extension operator \(\Pi _{\psi }\) generated via \(\psi \), and prove that \({\dot{B}}^{\alpha ,\lambda }_{p,p}({\mathbb {R}}^{n})\) can be extended to function spaces \({\mathscr {C}}^{\alpha }_{p,\lambda }({\mathbb {R}}^{n+1}_{+})\)

    更新日期:2020-05-24
  • Reducing Subspaces of Complex Symmetric Operators
    Complex Anal. Oper. Theory (IF 0.711) Pub Date : 2020-05-21
    Cun Wang, Sen Zhu

    An operator T on a separable, infinite dimensional, complex Hilbert space \({\mathcal {H}}\) is called complex symmetric if T has a symmetric matrix representation relative to some orthonormal basis for \({\mathcal {H}}\). This paper aims to describe reducing subspaces of complex symmetric operators from the view point of approximation. In particular, given a complex symmetric operator T, \(1\le n\le

    更新日期:2020-05-21
  • Geometric Properties of the Pentablock
    Complex Anal. Oper. Theory (IF 0.711) Pub Date : 2020-05-07
    Guicong Su

    In this paper, we give a positive answer to the question raised in Kosiński (Complex Anal Oper Theory 9(6):1349–1359, 2015) and Zapałowski (J Math Anal Appl 430(1):126–143, 2015), i.e., we show that the pentablock\({\mathcal {P}}\) is a \({\mathbb {C}}\)-convex domain.

    更新日期:2020-05-07
  • On a Singular Sylvester Equation with Unbounded Self-Adjoint A and B
    Complex Anal. Oper. Theory (IF 0.711) Pub Date : 2020-05-05
    Bogdan D. Djordjević

    In this paper we solve the Sylvester equation \(AX-XB=C\), where A and B are closed densely defined self-adjoint operators, and C is a linear operator. We obtain sufficient conditions for the existence of infinitely many solutions and we manage to classify them. These results generalize the previously known results regarding singular Sylvester equations. Finally, we illustrate our results on an operator

    更新日期:2020-05-05
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