Generic Bessel Potential Spaces on Lie Groups

Duván Cardona; Roland Duduchava; Arne Hendrickx; Michael Ruzhansky

doi:10.1007/978-3-031-62894-8_5

Generic Bessel Potential Spaces on Lie Groups

Duván Cardona
, Roland Duduchava^*
, Arne Hendrickx
, Michael Ruzhansky

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

2 Scopus citations

Abstract

The purpose of the present work is to define suitable (generic) Bessel Potential Spaces (GBPS) for convolution integro-differential equations (CIDE) on a Lie group G, which is homomorphic to the Euclidean space (formula presented). Is proved that ellipticity of the symbol is necessary condition for the Fredholm property of all CIDE in GBPS, but not sufficient. Ellipticity is sufficient condition for unique solvability of CIDE for p=2 and, for p≠2, only for CIDE with symbols from the subalgebra of l_p-multipliers.

Original language	English
Title of host publication	Trends in Mathematics
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	43-54
Number of pages	12
DOIs	https://doi.org/10.1007/978-3-031-62894-8_5
State	Published - 2024
Externally published	Yes

Publication series

Name	Trends in Mathematics
Volume	7
ISSN (Print)	2297-0215
ISSN (Electronic)	2297-024X

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.

Keywords

Convolution on Lie group
Generic Bessel potential spaces
Generic differential operators
Lie group

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/978-3-031-62894-8_5

Cite this

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abstract = "The purpose of the present work is to define suitable (generic) Bessel Potential Spaces (GBPS) for convolution integro-differential equations (CIDE) on a Lie group G, which is homomorphic to the Euclidean space (formula presented). Is proved that ellipticity of the symbol is necessary condition for the Fredholm property of all CIDE in GBPS, but not sufficient. Ellipticity is sufficient condition for unique solvability of CIDE for p=2 and, for p≠2, only for CIDE with symbols from the subalgebra of lp-multipliers.",

keywords = "Convolution on Lie group, Generic Bessel potential spaces, Generic differential operators, Lie group",

author = "Duv{\'a}n Cardona and Roland Duduchava and Arne Hendrickx and Michael Ruzhansky",

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T1 - Generic Bessel Potential Spaces on Lie Groups

AU - Cardona, Duván

AU - Duduchava, Roland

AU - Hendrickx, Arne

AU - Ruzhansky, Michael

PY - 2024

Y1 - 2024

N2 - The purpose of the present work is to define suitable (generic) Bessel Potential Spaces (GBPS) for convolution integro-differential equations (CIDE) on a Lie group G, which is homomorphic to the Euclidean space (formula presented). Is proved that ellipticity of the symbol is necessary condition for the Fredholm property of all CIDE in GBPS, but not sufficient. Ellipticity is sufficient condition for unique solvability of CIDE for p=2 and, for p≠2, only for CIDE with symbols from the subalgebra of lp-multipliers.

AB - The purpose of the present work is to define suitable (generic) Bessel Potential Spaces (GBPS) for convolution integro-differential equations (CIDE) on a Lie group G, which is homomorphic to the Euclidean space (formula presented). Is proved that ellipticity of the symbol is necessary condition for the Fredholm property of all CIDE in GBPS, but not sufficient. Ellipticity is sufficient condition for unique solvability of CIDE for p=2 and, for p≠2, only for CIDE with symbols from the subalgebra of lp-multipliers.

KW - Convolution on Lie group

KW - Generic Bessel potential spaces

KW - Generic differential operators

KW - Lie group

UR - https://www.scopus.com/pages/publications/85202586303

U2 - 10.1007/978-3-031-62894-8_5

DO - 10.1007/978-3-031-62894-8_5

M3 - Chapter

AN - SCOPUS:85202586303

T3 - Trends in Mathematics

SP - 43

EP - 54

BT - Trends in Mathematics

PB - Springer Science and Business Media Deutschland GmbH

ER -

Generic Bessel Potential Spaces on Lie Groups

Abstract

Publication series

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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Cite this