Distinguished representations and a Fourier summation formula

Distinguished positive regular representations

Let $G$ be a tamely ramified reductive $p$-adic‎ ‎group‎. ‎We study distinction of a class of irreducible admissible representations‎ ‎of $G$ by the group of fixed points $H$ of an involution‎ ‎of $G$‎. ‎The representations correspond to $G$-conjugacy classes of‎ ‎pairs $(T,phi)$‎, ‎where $T$ is a‎ ‎tamely ramified maximal torus of $G$ and $phi$ is a quasicharacter‎ ‎of $T$ whose restriction t...

Integrable Boehmians, Fourier Transforms, and Poisson’s Summation Formula

Boehmians are classes of generalized functions whose construction is algebraic. The first construction appeared in a paper that was published in 1981 [6]. In [8], P. Mikusiński constructs a space of Boehmians, βL1(R), in which each element has a Fourier transform. Mikusiński shows that the Fourier transform of a Boehmian satisfies some basic properties, and he also proves an inversion theorem. ...

Summation of Fourier Series

A general summability method of different orthogonal series is given with the help of an integrable function θ. As special cases the trigonometric Fourier, Walsh-, Walsh-Kaczmarz-, Vilenkinand Ciesielski-Fourier series and the Fourier transforms are considered. For each orthonormal system a different Hardy space is introduced and the atomic decomposition of these Hardy spaces are presented. A s...

Summation of Fourier

A Multiparameter Summation Formula for Theta Functions

We generalize Warnaar's elliptic extension of a Macdonald multi-parameter summation formula to Riemann surfaces of arbitrary genus. We start by a brief outline of the general theory of hypergeometric type series built from Jacobi theta functions [12, 13] (its extension to integrals [15] is not touched at all). Within this approach univariate elliptic hypergeometric series are defined as the ser...