Displaying similar documents to “Fourier-Wigner transforms and Liouville's theorems for the sub-Laplacian on the Heisenberg group”

Fourier transform of Schwartz functions on the Heisenberg group

Francesca Astengo, Bianca Di Blasio, Fulvio Ricci (2013)

Studia Mathematica

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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.

A characterization of Fourier transforms

Philippe Jaming (2010)

Colloquium Mathematicae

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The aim of this paper is to show that, in various situations, the only continuous linear (or not) map that transforms a convolution product into a pointwise product is a Fourier transform. We focus on the cyclic groups ℤ/nℤ, the integers ℤ, the torus 𝕋 and the real line. We also ask a related question for the twisted convolution.

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.

New existence results on nonhomogeneous Sturm-Liouville type BVPs for higher-order p-Laplacian differential equations

Yuji Liu (2011)

Applicationes Mathematicae

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A class of nonlinear boundary value problems for p-Laplacian differential equations is studied. Sufficient conditions for the existence of solutions are established. The nonlinearities are allowed to be superlinear. We do not apply the Green's functions of the relevant problem and the methods of obtaining a priori bounds for solutions are different from known ones. Examples that cannot be covered by known results are given to illustrate our theorems.

On Besov spaces and absolute convergence of the Fourier transform on Heisenberg groups

Leszek Skrzypczak (1998)

Commentationes Mathematicae Universitatis Carolinae

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In this paper the absolute convergence of the group Fourier transform for the Heisenberg group is investigated. It is proved that the Fourier transform of functions belonging to certain Besov spaces is absolutely convergent. The function spaces are defined in terms of the heat semigroup of the full Laplacian of the Heisenberg group.

On the support of Fourier transform of weighted distributions

Martha Guzmán-Partida (2010)

Commentationes Mathematicae Universitatis Carolinae

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We give sufficient conditions for the support of the Fourier transform of a certain class of weighted integrable distributions to lie in the region x 1 ≥ 0 and x 2 ≥ 0 .

A restriction theorem for the Heisenberg motion

P. Ratnakumar, Rama Rawat, S. Thangavelu (1997)

Studia Mathematica

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We prove a restriction theorem for the class-1 representations of the Heisenberg motion group. This is done using an improvement of the restriction theorem for the special Hermite projection operators proved in [13]. We also prove a restriction theorem for the Heisenberg group.