Related papers: A Whittaker-Plancherel Inversion Formula for $\mat…

Consider the Fourier transform on the group $GL(2,R)$ of real $2\times 2$-matrices. We show that Fourier-images of polynomial differential operators on $GL(2,R)$ are differential-difference operators with coefficients meromorphic in…

Given a unimodular real spherical space $Z=G/H$ we construct for each boundary degeneration $Z_I=G/H_I$ of $Z$ a Bernstein morphism $B_I: L^2(Z_I)_{\rm disc }\to L^2(Z)$. We show that $B:=\bigoplus_I B_I$ provides an isospectral…

We define an analog of the Poisson integral formula for a family of the non-commutative Lobachevsky spaces. The $q$-Fourier transform of the Poisson kernel is expressed through the $q$-Bessel-Macdonald function.

In this paper, a single sum formula for the linearization coefficients of the Bessel polynomials is given. In three special cases this formula reduces indeed to either Atia and Zeng's formula (Ramanujan Journal, Doi…

We develop the Riemann-Hilbert problem approach to inverse scattering for the two-dimensional Schrodinger equation at fixed energy. We obtain global or generic versions of the key results of this approach for the case of positive energy and…

We prove upper pointwise estimates for the Bergman kernel of the weighted Fock space of entire functions in $L^2(e^{-2\phi})$ where $\phi$ is a subharmonic function with $\Delta \phi$ a doubling measure. We derive estimates for the…

New index transforms with Weber type kernels, consisting of products of Bessel functions of the first and second kind are investigated. Mapping properties and inversion formulas are established for these transforms in Lebesgue spaces. The…

The Laplace transform is a useful and powerful analytic tool with applications to several areas of applied mathematics, including differential equations, probability and statistics. Similarly to the inversion of the Fourier transform,…

Using Bauer's expansion and properties of spherical Bessel and Legender functions, we deduce a new transform and briefly indicate its use.

In this paper, we generalize the weighted Fourier transform with respect to a function, originally proposed for the one-dimensional case in \cite{Dorrego}, to the $n$-dimensional Euclidean space $\mathbb{R}^{n}$. We develop a comprehensive…

The aim of this paper is to prove new uncertainty principles for an integral operator $\tt$ with a bounded kernel for which there is a Plancherel theorem. The first of these results is an extension of Faris's local uncertainty principle…

Using the theory of orthogonal polynomials, their associated recursion relations and differential formulas we develop a method for evaluating new integrals. The method is illustrated by obtaining a closed-form expression for the value of an…

Consider the Iwasawa decomposition of the real semisimple Lie group. The purpose of this paper is to define the Fourier transform in order to obtain the Plancherel theorem on its maxima solvable Lie group. Besides, we prove the existence…

We derive a Lorentzian OPE inversion formula for the principal series of $sl(2,\mathbb{R})$. Unlike the standard Lorentzian inversion formula in higher dimensions, the formula described here only applies to fully crossing-symmetric…

In this manuscript, we introduce the quadratic--phase Fourier--Bessel transform and develop its foundational properties, including continuity, the Riemann--Lebesgue lemma, reversibility, and Parseval's identity. We define the associated…

A strict integer Laurent polynomial in a variable $x$ is 0 or a sum of one or more terms having integer coefficients times $x$ raised to a negative integer exponent. Equations that can be transformed to certain such polynomials times…

We develop a unified approach for establishing rates of decay for the Fourier transform of a wide class of dynamically defined measures. Among the key features of the method is the systematic use of the $L^2$-flattening theorem obtained in…

Let $F$ be a $p$-adic field containing the full group of $n^{th}$ roots of 1 and let $ \widetilde{SL_2(F)}$ be the $n$-fold cover of $SL_2(F)$ constructed by Kubota. In this paper we compute the dimension of the space of Whittaker…

We use the newly developed technique of inverse quantum hamiltonian reduction to investigate the representation theory of the simple affine vertex algebra $\mathsf{A}_{2}(\mathsf{u},2)$ associated to $\mathfrak{sl}_{3}$ at level $\mathsf{k}…

We develop a general comparison result for inf convolution operators related to rearrangement. As a consequence we derive comparison results under spherically symmetric rearrangement for Laplace and polar transforms. As a by product we…