Related papers: Transmutations and Applications: a survey
We study the properties of different type of transforms by means of operational methods and discuss the relevant interplay with many families of special functions. We consider in particular the binomial transform and its generalizations. A…
Different types of convolution operations involving large Vandermonde matrices are considered. The convolutions parallel those of large Gaussian matrices and additive and multiplicative free convolution. First additive and multiplicative…
This is an expository paper on the subject of the title. It assumes basic scheme theory, commutative and homological algebra.
This paper contains a transcript of my presentation at the Wyant Tribute Symposium on August 2, 2021 at SPIE's Optics & Photonics conference in San Diego, California. The technical part of the paper has no overlap with a previous article of…
This is a survey of current and recent works on deformation quantization and index theorems.
This is a brief survey of recent results by the authors devoted to one of the most important operators of integral geometry. Basic facts about the analytic family of cosine transforms on the unit sphere and the corresponding Funk transform…
A representation for integral kernels of Delsarte transmutation operators is obtained in the form of a functional series with the exact formulas for the terms of the series. It is based on the application of hyperbolic pseudoanalytic…
Covariant vectors, Lyapunov vectors, or Oseledets vectors are increasingly being used for a variety of model analyses in areas such as partial differential equations, nonautonomous differentiable dynamical systems, and random dynamical…
Transformer architecture has widespread applications, particularly in Natural Language Processing and computer vision. Recently Transformers have been employed in various aspects of time-series analysis. This tutorial provides an overview…
This is a brief overview of the index hypergeometric transform (other terms for this integral operator are: Olevskii transform, Jacobi transform, generalized Mehler--Fock transform). We discuss applications of this transform to special…
The paper deals with singular Sturm-Liouville expressions with matrix-valued distributional coefficients. Due to a suitable regularization, the corresponding operators are correctly defined as quasi-differentials. Their resolvent…
We introduce a unified framework for the construction of convolutions and product formulas associated with a general class of regular and singular Sturm-Liouville boundary value problems. Our approach is based on the application of the…
We study the Liouville theory on a Riemann surface of genus g by means of their associated Drinfeld--Sokolov linear systems. We discuss the cohomological properties of the monodromies of these systems. We identify the space of solutions of…
We prove Marchenko-type uniqueness theorems for inverse Sturm-Liouville problems. Moreover, we prove a generalization of Ambarzumyans theorem.
In this paper, we get several new results on permutation polynomials over finite fields. First, by using the linear translator, we construct permutation polynomials of the forms $L(x)+\sum_{j=1}^k \gamma_jh_j(f_j(x))$ and…
This short paper being devoted to some aspects of the inverse problem of the representation theory treats several themes, which have their origins in the researches of F.A.Berezin, D.P.Zhelobenko, V.P.Maslov and his group, in context of the…
We develop tools for the analysis of fronts, pulses, and wave trains in spatially extended systems with nonlocal coupling. We first determine Fredholm properties of linear operators, thereby identifying pointwise invertibility of the…
When is it possible to interpret a given Markov process as a L\'evy-like process? Since the class of L\'evy processes can be defined by the relation between transition probabilities and convolutions, the answer to this question lies in the…
The book contains the results obtained by the author in 1975-1982 and presents new constructive methods of the topological analysis of integrable systems having non-linear integrals in involution. The phase topology of the classical…
This expository paper, based on a Current Events Bulletin talk at the January, 2016 Joint Meetings, introduces the concept of Lyapunov exponents and discusses the role they play in three areas: smooth ergodic theory, Teichm\"uller theory,…