Tsukuba Journal of Mathematics

A characterization of the tempered distributions supported by a regular closed set in the Heisenberg group

Yasuyuki Oka

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Abstract

The aim of this paper is to give a characterization of the tempered distributions supported by a (Whitney's) regular closed set in the Euclidean space and the Heisenberg group by means of the heat kernel method. The heat kernel method, introduced by T. Matsuzawa, is the method to characterize the generalized functions on the Euclidean space by the initial value of the solutions of the heat equation.

Article information

Source
Tsukuba J. Math., Volume 39, Number 1 (2015), 97-119.

Dates
First available in Project Euclid: 7 August 2015

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1438951819

Digital Object Identifier
doi:10.21099/tkbjm/1438951819

Mathematical Reviews number (MathSciNet)
MR3383880

Zentralblatt MATH identifier
06486344

Subjects
Primary: 46F05: Topological linear spaces of test functions, distributions and ultradistributions [See also 46E10, 46E35] 46F15: Hyperfunctions, analytic functionals [See also 32A25, 32A45, 32C35, 58J15] 81S30: Phase-space methods including Wigner distributions, etc.

Keywords
Tempered distributions in the Heisenberg group Heat equation regular closed sets in the Heisenberg group

Citation

Oka, Yasuyuki. A characterization of the tempered distributions supported by a regular closed set in the Heisenberg group. Tsukuba J. Math. 39 (2015), no. 1, 97--119. doi:10.21099/tkbjm/1438951819. https://projecteuclid.org/euclid.tkbjm/1438951819


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