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Holomorphic solutions and solvability theory for a class of linear complete singular integro-differential equations with convolution by Riemann–Hilbert method
In this article, we investigate a class of linear complete singular integro-differential equations of convolution type with Fredholm integral...
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Riemann–Hilbert method for multi-soliton solutions of a fifth-order nonlinear Schrödinger equation
A fifth-order nonlinear Schrödinger equation which describes the one-dimensional anisotropic Heisenberg ferromagnetic spin chain is under...
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On the Structure of the Spectrum and the Resolvent Set of a Toeplitz Operator in a Countably Normed Space of Smooth Functions
AbstractIn the countably normed space of smooth functions on the unit circle, we consider a Toeplitz operator with a smooth symbol. Questions...
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Stability Analysis of a Simple Discretization Method for a Class of Strongly Singular Integral Equations
Motivated by the discrete dipole approximation (DDA) for the scattering of electromagnetic waves by a dielectric obstacle that can be considered as a...
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mu-Brownian Motion, Dualities, Diffusions, Transforms, and Reproducing Kernel Hilbert Spaces
Replacing the Lebesgue measure on an interval by a Stieltjes positive non-atomic measure, we study the corresponding counterpart of the Brownian...
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On the Bloch–Kato conjecture for Hilbert modular forms
The aim of this paper is to prove inequalities towards instances of the Bloch–Kato conjecture for Hilbert modular forms of parallel weight two, when...
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Inhomogeneous Hilbert Boundary-Value Problem with a Finite Number of Second-Type Singularity Points
In this paper, we describe the inhomogeneous Hilbert boundary-value problem of the theory of analytic functions with an infinite index and a boundary...
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Systems of two subspaces in a Hilbert space
We study two subspace systems in a separable infinite-dimensional Hilbert space up to (bounded) isomorphism. One of the main result of this paper is...
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Stochastic proximal gradient methods for nonconvex problems in Hilbert spaces
For finite-dimensional problems, stochastic approximation methods have long been used to solve stochastic optimization problems. Their application to...
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Two new self-adaptive algorithms for solving the split common null point problem with multiple output sets in Hilbert spaces
To solve the split common null point problem with multiple output sets in Hilbert spaces, we introduce two new self-adaptive algorithms and prove...
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Weighted Composition Operators That Preserve Frames On Weighted Hardy Spaces
In this paper, we characterize weighted composition operators that preserve frames on the weighted Hardy spaces in the unit disk. In particular, we...
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Positivity results for Weyl’s pseudo-differential calculus on the Wiener space
This paper deals with positivity properties for a pseudo-differential calculus, generalizing Weyl’s classical quantization, and set on an infinite...
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Ramsey Theory Before Ramsey: Hilbert’s Theorem
A new theory often appears in an attempt to answer new questions or to shed a new light on old problems. It is not usually born overnight. Before its...