Fourier transform of Schwartz functions on the Heisenberg group

Francesca Astengo; Bianca Di Blasio; Fulvio Ricci

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Displaying similar documents to “Fourier transform of Schwartz functions on the Heisenberg group”

A spherical transform on Schwartz functions on the Heisenberg group associated to the action of U(p,q)

T. Godoy, L. Saal (2006)

Colloquium Mathematicae

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Let 𝓢(Hₙ) be the space of Schwartz functions on the Heisenberg group Hₙ. We define a spherical transform on 𝓢(Hₙ) associated to the action (by automorphisms) of U(p,q) on Hₙ, p + q = n. We determine its kernel and image and obtain an inversion formula analogous to the Godement-Plancherel formula.

The Heisenberg group and the group Fourier transform of regular homogeneous distributions

Susan Slome (2000)

Studia Mathematica

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On the Fourier transform, Boehmians, and distributions

Dragu Atanasiu, Piotr Mikusiński (2007)

Colloquium Mathematicae

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We introduce some spaces of generalized functions that are defined as generalized quotients and Boehmians. The spaces provide simple and natural frameworks for extensions of the Fourier transform.

Boehmians of type S and their Fourier transforms

R. Bhuvaneswari, V. Karunakaran (2010)

Annales UMCS, Mathematica

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Function spaces of type S are introduced and investigated in the literature. They are also applied to study the Cauchy problem. In this paper we shall extend the concept of these spaces to the context of Boehmian spaces and study the Fourier transform theory on these spaces. These spaces enable us to combine the theory of Fourier transform on these function spaces as well as their dual spaces.

Boehmians of type S and their Fourier transforms

R. Bhuvaneswari, V. Karunakaran (2010)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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Spherical means on the Heisenberg group and a restriction theorem for the symplectic Fourier transform.

Sundaram Thangavelu (1991)

Revista Matemática Iberoamericana

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The aim of this paper is to study mean value operators on the reduced Heisenberg group H/Γ, where H is the Heisenberg group and Γ is the subgroup {(0,2πk): k ∈ Z} of H.

The Fourier Transform of Harish-Chandra's c-Function and Inversion of the Able Transform.

R.J. Beerends (1987)

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The Fourier transform of distributions and the exchange formula

B. Fisher, Li Chen Kuan, A. Takači (1988)

Matematički Vesnik

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Fourier-Wigner transforms and Liouville's theorems for the sub-Laplacian on the Heisenberg group

Aparajita Dasgupta, M. W. Wong (2010)

Banach Center Publications

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The sub-Laplacian on the Heisenberg group is first decomposed into twisted Laplacians parametrized by Planck's constant. Using Fourier-Wigner transforms so parametrized, we prove that the twisted Laplacians are globally hypoelliptic in the setting of tempered distributions. This result on global hypoellipticity is then used to obtain Liouville's theorems for harmonic functions for the sub-Laplacian on the Heisenberg group.