Invariant generalized functions supported on an orbit

DOI10.1007/s11856-018-1668-2zbMath1394.22013arXiv1701.00411OpenAlexW2963146131MaRDI QIDQ1650041

Dmitry Gourevitch, Avraham Aizenbud

Publication date: 29 June 2018

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.00411

zbMATH Keywords

distributiongeneralized functionNash manifoldNash groupNash stack, algebraic group

Mathematics Subject Classification ID

Geometric invariant theory (14L24) Operations with distributions and generalized functions (46F10) Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45)

Cites Work

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• Multiplicity one theorems
• The de-Rham theorem and Shapiro lemma for Schwartz functions on Nash manifolds
• The Schwartz space of a smooth semi-algebraic stack
• Generalized Harish-Chandra descent, Gelfand pairs, and an Archimedean analog of Jacquet-Rallis's theorem. With an appendix by the authors and Eitan Sayag.
• Multiplicity one theorems: the Archimedean case
• Multiplicity one theorem for \((\text{GL}_{n+1}({\mathbb{R}}), \text{GL}_{n} ({ \mathbb{R}}))\)
• The multiplicity one theorem for \(\mathrm{GL}_n\)
• A proof of Kirillov's conjecture
• On the transverse symbol of vectorial distributions and some applications to harmonic analysis
• Schwartz Functions on Nash Manifolds
• Smooth transfer of Kloosterman integrals (the Archimedean case)
• Invariant Eigendistributions on a Semisimple Lie Group
• Invariant eigendistributions on semisimple Lie groups

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