Wiener Tauberian theorem for hypergeometric transforms

A genuine analogue of Wiener Tauberian theorem for $ \mathrm {SL}(2, \R)$

We prove a genuine analogue of Wiener Tauberian theorem for integrable functions on $\mathrm {SL}(2, \R).$

Analogues of the Wiener-Tauberian and Schwartz theorems for radial functions on symmetric spaces

We prove a Wiener-Tauberian theorem for $L^1$-spherical functions on a semisimple Lie group of arbitrary real rank. We also establish a Schwartz theorem for complex groups. As a corollary we obtain a Wiener-Tauberian type theorem for for compactly supported distributions.

The Paley-Wiener-Gelfand tauberian theorem for semigroups with invariant measure

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.

Wiener Tauberian theorem for rank one semisimple Lie groups

We prove a genuine analogue of Wiener Tauberian theorem for $L^1(G//K)$, where G is a semisimple Lie group of real rank one. This generalizes the corresponding result on the automorphism group of the unit disk by Y. Ben Natan, Y. Benyamini, H. Hedenmalm and Y. Weit.

经典与量子调和分析中的Wiener Tauberian定理

Wiener's Tauberian theorem in classical and quantum harmonic analysis

本文从极限函数视角研究Wiener Tauberian定理，提出多个新版本，并证明了量子调和分析意义下的算子类似定理，进而刻画了严格大于紧算子类的慢振荡算子类，最后探讨了统一版本及其应用。

A Wiener Tauberian theorem for operators and functions

We prove variants of Wiener's Tauberian theorem in the framework of quantum harmonic analysis, i.e. for convolutions between an absolutely integrable function and a trace class operator, or of two trace class operators. Our results include Wiener's Tauberian theorem as a special case. Applications of our Tauberian theorems are related to localization operators, Toeplitz operators, isomorphism theorems between Bargmann-Fock spaces and quantization schemes with consequences for Shubin's pseudodifferential operator calculus and Born-Jordan quantization. Based on the links between localization ope…