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Discrete analogs of the Lebedev transforms with the product of the modified Bessel functions are introduced and investigated. Several expansions of suitable functions and sequences in terms of the series and integrals, involving the…
Polynomial, or Delsarte's, method in coding theory accounts for a variety of structural results on, and bounds on the size of, extremal configurations (codes and designs) in various metric spaces. In recent works of the authors the…
New index transforms, involving the real part of the modified Bessel function of the first kind as the kernel are considered. Mapping properties such as the boundedness and invertibility are investigated for these operators in the Lebesgue…
The objective of this study is to ascertain the existence and forms of the finite order meromorphic and entire functions of several complex variables satisfying some certain Fermat-type partial differential-difference equations by…
We observe that solutions of a large class of highly oscillatory second order linear ordinary differential equations can be approximated using nonoscillatory phase functions. In addition, we describe numerical experiments which illustrate…
An approximation result for the bilinear Hilbert transform is proved and used for the inversion of the bilinear Hilbert transform. Also, p-Lebesgue points $(p\geq 1)$ are analyzed.
Parameter identification problems in partial differential equations (PDEs) consist in determining one or more functional coefficient in a PDE. In this article, the Bayesian nonparametric approach to such problems is considered. Focusing on…
In this paper we presents further developments regarding the enrichment of the basic Theory of Order Completion. In particular, spaces of generalized functions are constructed that contain generalized solutions to all systems of continuous,…
Reciprocal transformations mix the role of the dependent and independent variables of (nonlinear partial) differential equations to achieve simpler versions or even linearized versions of them. These transformations help in the…
We discuss a purely variational approach to the study of a wide class of second order nonhomogeneous dissipative hyperbolic PDEs. Precisely, we focus on the wave-like equations that present also a nonzero source term and a…
Transformations of differential equations to other equivalent equations play a central role in many routines for solving intricate equations. A class of differential equations that are particularly amenable to solution techniques based on…
Part I. Some Facts From p-Adic Analysis. Part II. Tables of Integrals.
A geometric approach to Sundman transformation defined by basic functions for systems of second-order differential equations is developed and the necessity of a change of the tangent structure by means of the function defining the Sundman…
Analytic continuation and functional equation of a Dirichlet series constructed from two (not necessarily cuspidal) holomorphic modular forms is discussed, where either weights of the modular forms or characters are not necessarily equal to…
Partial Differential Equations (PDEs) have long been recognized as powerful tools for image processing and analysis, providing a framework to model and exploit structural and geometric properties inherent in visual data. Over the years,…
This paper is about elliptic and parabolic partial differential operators with discontinuities in the gradient which are compatible with a Finsler norm in a sense to be made precise. Examples of this type of problems arise in a number of…
We introduce suitable coordinate systems for pipes and their variants that allow us to transform partial differential equations (PDEs) on the pipe surfaces or in the solid pipes into computational domains with fixed limits/ranges. Such a…
Independently trained transformers compute the same function in residual-stream bases that differ by a uniform random rotation on $\mathrm{SO}(d_{\mathrm{model}})$. We call this phenomenon polymorphism: same function, mutually…
We begin with (densely-defined) fractional linear transformations (FLT) on (some) Banach algebras and their relatives. This leads to Wedderburn's continued fractions (recursively-defined noncommutative polynomials) for any ring. Along the…
Partial differential equations (PDEs) involving fractional Laplace operators have been increasingly used to model non-local diffusion processes and are actively investigated using both analytical and numerical approaches. The purpose of…