Fourier transform of Schwartz functions on the Heisenberg group

• Autorzy: Francesca Astengo , Bianca Di Blasio , Fulvio Ricci
• Języki publikacji: EN

Abstrakty

EN

Let H₁ be the 3-dimensional Heisenberg group. We prove that a modified version of the spherical transform is an isomorphism between the space 𝓢ₘ(H₁) of Schwartz functions of type m and the space 𝓢(Σₘ) consisting of restrictions of Schwartz functions on ℝ² to a subset Σₘ of the Heisenberg fan with |m| of the half-lines removed. This result is then applied to study the case of general Schwartz functions on H₁.

Kategorie tematyczne

• 43A80: Analysis on other specific Lie groups
• 22E25: Nilpotent and solvable Lie groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2013
• Tom: 214
• Numer: 3
• Strony: 201-222

Daty

wydano

2013

Twórcy

autor

Francesca Astengo

• Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, 16146 Genova, Italy

autor

Bianca Di Blasio

• Dipartimento di Matematica e Applicazioni, Università degli Studi di Milano-Bicocca, Via Cozzi 53, 20125 Milano, Italy

autor

Fulvio Ricci

• Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy

Identyfikatory

DOI

10.4064/sm214-3-1