相关论文: Paley-Wiener theorems for the $\Theta$-spherical t…
This paper presents necessary, sufficient, and equivalent conditions for the spherical convexity of non-homogeneous quadratic functions. In addition to motivating this study and identifying useful criteria for determining whether such…
The paper contains the inversion formula for the weighted spherical mean. The interest to reconstruction a function by its integral by sphere grews tremendously in the last six decades, stimulated by the spectrum of new problems and methods…
The connection between spherical harmonics and symmetric tensors is explored. For each spherical harmonic, a corresponding traceless symmetric tensor is constructed. These tensors are then extended to include nonzero traces, providing an…
In this paper we introduce appropriate associated function to the sequence $M_p=p^{\t p^{\s}}$, $p\in \N$, $\t>0$, $\s>1$, and derive its sharp asymptotic estimates in terms of the Lambert $W$ function. These estimates are used to prove a…
A class of quantum analogues of compact symmetric spaces of classical type is introduced by means of constant solutions to the reflection equations. Their zonal spherical functions are discussed in connection with $q$-orthogonal…
The classical theory of symmetric functions has a central position in algebraic combinatorics, bridging aspects of representation theory, combinatorics, and enumerative geometry. More recently, this theory has been fruitfully extended to…
Given a quadratic CR manifold $\mathcal{M}$ embedded in a complex space, we study Paley-Wiener-Schwartz theorems for spaces of Schwartz functions and tempered distributions on $\mathcal{M}$.
We study path integrals in the Trotter-type form for the Schr\"odinger equation, where the Hamiltonian is the Weyl quantization of a real-valued quadratic form perturbed by a potential $V$ in a class encompassing that - considered by…
The symmetric function theorem states that a polynomial that is invariant under permutation of variables, is a polynomial in the elementary symmetric polynomials. We deduce this classical result, in the analytic setting, from the…
We define the radiation fields of solutions to critical semilinear wave equations in R^3 and use them to define the scattering operator. We also prove a support theorem for the radiation fields with radial initial data. This extends the…
This paper presents recent results obtained by the authors (partly in collaboration with A. Dabrowska) concerning expansions of zonal functions on Euclidean spheres into spherical harmonics and some applications of such expansions for…
We use the classical Fourier analysis to introduce analytic families of weighted differential operators on the unit sphere. These operators are polynomial functions of the usual Beltrami-Laplace operator. New inversion formulas are obtained…
Plancherel formula is one of the celebrated result of harmonic analysis on semisimple Lie groups and their homogeneous spaces. The main goal of this work is to find a q-analog of the Plancherel formula for spherical transform the unit…
We explicitly establish a unitary correspondence between spherical irreducible tensor operators and cartesian tensor operators of any rank. That unitary relation is implemented by means of a basis of integer-spin wave functions that…
In this paper we introduce the concept of a convolution type operation of functionals on Wiener space. It contains several kinds of the concepts of convolution products on Wiener space, which have been studied by many authors. We then…
Quantum harmonic analysis on phase space is shown to be linked with localization operators. The convolution between operators and the convolution between a function and an operator provide a conceptual framework for the theory of…
We generalize the definition of convolution of vectors and tensors on the 2-sphere, and prove that it commutes with differential operators. Moreover, vectors and tensors that are normal/tangent to the spherical surface remain so after the…
Langlands posed the question of whether a local functorial transfer map of stable tempered characters can be interpolated by the transpose of a linear operator between spaces of stable orbital integrals of test functions. These so-called…
A general construction of transmutation operators is developed for selfadjoint operators in Gelfand triples. Theorems regarding analyticity of generalized eigenfunctions and Paley-Wiener properties are proved.
The goal of this paper is to introduce the notion of polyconvolution for Fourier-cosine, Laplace integral operators, and its applications. The structure of this polyconvolution operator and associated integral transforms are investigated in…