Related papers: The Integral Transform of N.I.Akhiezer
An integral transformation relating two inequalities in Khabibullin's conjecture is found. Another proof of this conjecture for some special values of its numeric parameters is suggested.
In analogy with the classical theory of Eichler integrals for integral weight modular forms, Lawrence and Zagier considered examples of Eichler integrals of certain half-integral weight modular forms. These served as early prototypes of a…
The $p$-adic $q$-integral (= $I_q$-integral) was defined by author in the previous paper [1, 3]. In this paper, we consider $I_q$-Fourier transform and investigate some properties which are related to this transform.
We develop the Akhiezer iteration, a generalization of the classical Chebyshev iteration, for the inner product-free, iterative solution of indefinite linear systems using orthogonal polynomials for measures supported on multiple, disjoint…
This version has been withdrawn. The new and final version is on ArXiv 1103.4878
An exploration into the uses of the Fourier transform in the areas of algebraic and arithmetic geometry. In particular this treats the topics of Banach-Colmez spaces, for which an introduction to the theory of perfectoid spaces is given.…
We establish an explicit form of the Backlund transformation for the most known integrable systems.
A simple integral formula as an iterated residue is presented for the Baker-Akhiezer function related to $A_n$ type root system both in the rational and trigonometric cases. We present also a formula for the Baker-Akhiezer function as a…
Basic elements of integral calculus over algebras of iterated differential forms, are presented. In particular, defining complexes for modules of integral forms are described and the corresponding berezinians and complexes of integral forms…
This book deals with the theory of generalized algebraic transformations, which is elaborated with the aim to provide a relatively simple theoretical tool that enables an exact treatment of diverse more complex lattice-statistical models.…
This paper is an introductory text to the theory of $q$-deformed Fourier transforms, as first discussed by Rogov and Olshanetsky. We derive the well-known results in detail, present them in a format that suits our needs, and include some…
We propose a new integral based on Taylor measures, study its properties extensively, and we illustrate that it includes many concepts from mathematics as special cases. In particular, the new integral emerges as a generalization of the…
In this current article, we introduce the quadruple Shehu transform and its inverse. We also introduce some properties of quadruple Shehu transform. The Convolution theorem and its proof are also discussed. Further, to solve homogeneous and…
An algebraic deformation theory of algebras over the Landweber-Novikov algebra is obtained.
Using Bauer's expansion and properties of spherical Bessel and Legender functions, we deduce a new transform and briefly indicate its use.
We give integral presentations of quantum lattice Heisenberg algebras by viewing them as Heisenberg doubles. Our presentations generalize those appearing previously in the literature.
We introduce a complex q-Fourier transform as a generalization of the (real) one analyzed in [Milan J. Math. {\bf 76} (2008) 307]. By recourse to tempered ultradistributions we show that this complex plane-generalization overcomes all…
In the paper, the authors find some integral representations and discover some properties of Lah numbers.
In this paper we study those polynomials orthogonal with respect to a particular weight over the union of disjoint intervals first introduced by N.I. Akhiezer, via a reformulation as a matrix factorization or Riemann-Hilbert problem. This…
Further formulas are presented involving quantum mechanics, thermodynamics, and integrable systems. Modifications of dispersionless theory are developed.