The Semigroup and the Inverse of the Laplacian on the Heisenberg Group

By decomposing the Laplacian on the Heisenberg group into a family of parametrized partial differential operators Lt ,t ∈ R \ {0}, and using parametrized Fourier-Wigner transforms, we give formulas and estimates for the strongly continuous one-parameter semigroup generated by Lt, and the i...

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Autores principales:	DASGUPTA,APARAJITA, WONG,M.W
Lenguaje:	English
Publicado:	Universidad de La Frontera. Departamento de Matemática y Estadística. 2010
Materias:	Heisenberg group Laplacian parametrized partial differential operators Hermite functions Fourier-Wigner transforms heat equation one parameter semigroup inverse of Laplacian Sobolev spaces
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462010000300006
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spelling	oai:scielo:S0719-064620100003000062018-10-08The Semigroup and the Inverse of the Laplacian on the Heisenberg GroupDASGUPTA,APARAJITAWONG,M.W Heisenberg group Laplacian parametrized partial differential operators Hermite functions Fourier-Wigner transforms heat equation one parameter semigroup inverse of Laplacian Sobolev spaces By decomposing the Laplacian on the Heisenberg group into a family of parametrized partial differential operators Lt ,t ∈ R \ {0}, and using parametrized Fourier-Wigner transforms, we give formulas and estimates for the strongly continuous one-parameter semigroup generated by Lt, and the inverse of Lt . Using these formulas and estimates, we obtain Sobolev estimates for the one-parameter semigroup and the inverse of the Laplacian.info:eu-repo/semantics/openAccessUniversidad de La Frontera. Departamento de Matemática y Estadística.Cubo (Temuco) v.12 n.3 20102010-01-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462010000300006en10.4067/S0719-06462010000300006
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Heisenberg group Laplacian parametrized partial differential operators Hermite functions Fourier-Wigner transforms heat equation one parameter semigroup inverse of Laplacian Sobolev spaces
spellingShingle	Heisenberg group Laplacian parametrized partial differential operators Hermite functions Fourier-Wigner transforms heat equation one parameter semigroup inverse of Laplacian Sobolev spaces DASGUPTA,APARAJITA WONG,M.W The Semigroup and the Inverse of the Laplacian on the Heisenberg Group
description	By decomposing the Laplacian on the Heisenberg group into a family of parametrized partial differential operators Lt ,t ∈ R \ {0}, and using parametrized Fourier-Wigner transforms, we give formulas and estimates for the strongly continuous one-parameter semigroup generated by Lt, and the inverse of Lt . Using these formulas and estimates, we obtain Sobolev estimates for the one-parameter semigroup and the inverse of the Laplacian.
author	DASGUPTA,APARAJITA WONG,M.W
author_facet	DASGUPTA,APARAJITA WONG,M.W
author_sort	DASGUPTA,APARAJITA
title	The Semigroup and the Inverse of the Laplacian on the Heisenberg Group
title_short	The Semigroup and the Inverse of the Laplacian on the Heisenberg Group
title_full	The Semigroup and the Inverse of the Laplacian on the Heisenberg Group
title_fullStr	The Semigroup and the Inverse of the Laplacian on the Heisenberg Group
title_full_unstemmed	The Semigroup and the Inverse of the Laplacian on the Heisenberg Group
title_sort	semigroup and the inverse of the laplacian on the heisenberg group
publisher	Universidad de La Frontera. Departamento de Matemática y Estadística.
publishDate	2010
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462010000300006
work_keys_str_mv	AT dasguptaaparajita thesemigroupandtheinverseofthelaplacianontheheisenberggroup AT wongmw thesemigroupandtheinverseofthelaplacianontheheisenberggroup AT dasguptaaparajita semigroupandtheinverseofthelaplacianontheheisenberggroup AT wongmw semigroupandtheinverseofthelaplacianontheheisenberggroup
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The Semigroup and the Inverse of the Laplacian on the Heisenberg Group

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