相关论文: Paley-Wiener theorems for the $\Theta$-spherical t…

The aim of this paper is to show a connection between an extended theory of statistical experiments on the one hand and the foundation of quantum theory on the other hand. The main aspects of this extension are: One assumes a hyperparameter…

This note concerns exponential sheaves and the "universal" Fourier transform on them. Fourier invertibility and the subsequent Fourier miracle is demonstrated. Further, t-structures and realizations are constructed and shown to have…

Spin-weighted spherical functions provide a useful tool for analyzing tensor-valued functions on the sphere. A tensor field can be decomposed into complex-valued functions by taking contractions with tangent vectors on the sphere and the…

Wannier functions have widespread utility in condensed matter physics and beyond. Topological physics, on the other hand, has largely involved the related notion of compactly-supported Wannier-type functions, which arise naturally in flat…

We consider the image of the operator inducing the determinantal point process with the confluent hypergeometric kernel. The space is described as the image of $L_2[0, 1]$ under a unitary transform, which generalizes the Fourier transform.…

We introduce and develop the notion of spherical polyharmonics, which are a natural generalisation of spherical harmonics. In particular we study the theory of zonal polyharmonics, which allows us, analogously to zonal harmonics, to…

Let $M$ be a Riemmanian manifold with bounded geometry. We consider a generalization of Paley-Wiener functions and Lagrangian splines on $M$. An analog of the Paley-Wiener theorem is given. We also show that every Paley-Wiener function on a…

We introduce the multiple zeta functions with structures similar to those of symmetric functions such as Schur $P$-, Schur $Q$-, symplectic and orthogonal functions in the representation theory. We first consider their basic properties such…

The theorem is proved that generalizes the Gelfand generalization of the Paley-Wiener tauberian theorem to general abelian topological semigroups with invariant measure. Several corollaries of this theorem are given.

The spherically symmetric static solutions are searched for in some f(T) models of gravity theory with a Maxwell term. To do this, we demonstrate that reconstructing the Lagrangian of f(T) theories is sensitive to the choice of frame, and…

We argue that a proof of the geometrical form of the Paley-Wiener theorems for the Dunkl transform in the literature is not correct.

In many applications data are measured or defined on a spherical manifold; spherical harmonic transforms are then required to access the frequency content of the data. We derive algorithms to perform forward and inverse spin spherical…

Let $f$ be a Paley-Wiener function in the space $L_{2}(X)$, where $X$ is a symmetric space of noncompact type. It is shown that by using the values of $f$ on a sufficiently dense and separated set of points of $X$ one can give an exact…

Spaces of infinitely differentiable functions on ${\mathbb R}^n$ (more general than Gelfand-Shilov spaces of type $W_M$) are considered in the article. Paley-Wiener type theorems are obtained.

An analog of the Paley-Wiener isomorphism for the Hardy space with an invariant measure over infinite-dimensional unitary groups is described. This allows us to investigate on such space the shift and multiplicative groups, as well as,…

A theoretical scheme, based on a probabilistic generalization of the Hamilton's principle, is elaborated to obtain an unified description of more general dynamical behaviors determined both from a lagrangian function and by mechanisms not…

We investigate Wiener's Tauberian theorem from the perspective of limit functions, which results in several new versions of the Tauberian theorem. Based on this, we formulate and prove analogous Tauberian theorems for operators in the sense…

Spherical Harmonics, $Y_\ell^m(\theta,\phi)$, are derived and presented (in a Table) for half-odd-integer values of $\ell$ and $m$. These functions are eigenfunctions of $L^2$ and $L_z$ written as differential operators in the…

This article presents an exhaustive classification of metric-affine theories according to their scale symmetries. First it is clarified that there are three relevant definitions of a scale transformation. These correspond to a projective…

Lichnerowicz's algebra of differential geometric operators acting on symmetric tensors can be obtained from generalized geodesic motion of an observer carrying a complex tangent vector. This relation is based upon quantizing the classical…