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dc.contributor.author
Gallo, Andrea Lilén  
dc.contributor.author
Saal, Linda Victoria  
dc.date.available
2021-10-13T18:36:25Z  
dc.date.issued
2020-09  
dc.identifier.citation
Gallo, Andrea Lilén; Saal, Linda Victoria; Some harmonic analysis on commutative nilmanifolds; Heldermann Verlag; Journal Of Lie Theory; 30; 3; 9-2020; 673-690  
dc.identifier.issn
0949-5932  
dc.identifier.uri
http://hdl.handle.net/11336/143438  
dc.description.abstract
In this work, we consider a family of Gelfand pairs (KnN, N) (inshort (K, N) ) where Nis a two step nilpotent Lie group, and Kis the group oforthogonal automorphisms ofN. This family has a nice analytic property: almos tall these 2-step nilpotent Lie group have square integrable representations. In these cases, following Moore-Wolf’s theory, we find an explicit expression for the inversion formula of N, and as a consequence, we decompose the regular action ofKnNonL2(N). This explicit expression for the Fourier inversion formula of N, specializedto a class of commutative nilmanifolds described by J. Lauret, sharpens the recent analysis due to J. Wolf concerning the regular action ofKnNonL2(N) . When Nis the Heisenberg group, we obtain the decomposition ofL2(N) under the action of KnN for all Ksuch that (K, N) is a Gelfand pair. Finally, we also give aparametrization for the generic spherical functions associated to the pair (K, N) ,and we give an explicit expression for these functions in some cases  
dc.format
application/pdf  
dc.language.iso
eng  
dc.publisher
Heldermann Verlag  
dc.rights
info:eu-repo/semantics/restrictedAccess  
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/  
dc.subject
GELFAND PAIRS  
dc.subject
INVERSION FORMULA  
dc.subject
NILPOTENT GROUP  
dc.subject
REGULAR REPRESENTATION  
dc.subject.classification
Matemática Pura  
dc.subject.classification
Matemáticas  
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS  
dc.title
Some harmonic analysis on commutative nilmanifolds  
dc.type
info:eu-repo/semantics/article  
dc.type
info:ar-repo/semantics/artículo  
dc.type
info:eu-repo/semantics/publishedVersion  
dc.date.updated
2021-09-06T15:09:25Z  
dc.journal.volume
30  
dc.journal.number
3  
dc.journal.pagination
673-690  
dc.journal.pais
Alemania  
dc.journal.ciudad
Lemgo  
dc.description.fil
Fil: Gallo, Andrea Lilén. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina  
dc.description.fil
Fil: Saal, Linda Victoria. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina  
dc.journal.title
Journal Of Lie Theory  
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1909.09873  
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.heldermann.de/JLT/JLT30/JLT303/jlt30035.htm