Matches in SemOpenAlex for { <https://semopenalex.org/work/W4288302912> ?p ?o ?g. }
Showing items 1 to 77 of
77
with 100 items per page.
- W4288302912 abstract "The Harish-Chandra Fourier transform, $fmapstomathcal{H}f,$ is a linear topological algebra isomorphism of the spherical (Schwartz) convolution algebra $mathcal{C}^{p}(G//K)$ (where $K$ is a maximal compact subgroup of any arbitrarily chosen group $G$ in the Harish-Chandra class and $0<pleq2$) onto the (Schwartz) multiplication algebra $bar{mathcal{Z}}({mathfrak{F}}^{epsilon})$ (of $mathfrak{w}-$invariant members of $mathcal{Z}({mathfrak{F}}^{epsilon}),$ with $epsilon=(2/p)-1$). This is the well-known Trombi-Varadarajan theorem for spherical functions on the real reductive group, $G.$ Even though $mathcal{C}^{p}(G//K)$ is a closed subalgebra of $mathcal{C}^{p}(G),$ a similar theorem cannot however be proved for the full Schwartz convolution algebra $mathcal{C}^{p}(G)$ except; for $mathcal{C}^{p}(G/K)$ (whose method is essentially that of Trombi-Varadarajan, as shown by M. Eguchi); for few specific examples of groups (notably $G=SL(2,R)$) and; for some notable values of $p$ (with restrictions on $G$ and/or on members of $;mathcal{C}^{p}(G)$). In this paper, we construct an appropriate image of the Harish-Chandra Fourier transform for the full Schwartz convolution algebra $mathcal{C}^{p}(G),$ without any restriction on any of $G,p$ and members of $;mathcal{C}^{p}(G).$ Our proof, that the Harish-Chandra Fourier transform, $fmapstomathcal{H}f,$ is a linear topological algebra isomorphism on $mathcal{C}^{p}(G),$ equally shows that its image $mathcal{C}^{p}(widehat{G})$ can be nicely decomposed, that the full invariant harmonic analysis is available and implies that the definition of the Harish-Chandra Fourier transform may now be extended to include all $p-$tempered distributions on $G$ and to the zero-Schwartz spaces" @default.
- W4288302912 created "2022-07-28" @default.
- W4288302912 creator A5064320583 @default.
- W4288302912 date "2019-06-26" @default.
- W4288302912 modified "2023-09-29" @default.
- W4288302912 title "Non-spherical Harish-Chandra Fourier transforms on real reductive groups" @default.
- W4288302912 doi "https://doi.org/10.48550/arxiv.1907.00717" @default.
- W4288302912 hasPublicationYear "2019" @default.
- W4288302912 type Work @default.
- W4288302912 citedByCount "0" @default.
- W4288302912 crossrefType "posted-content" @default.
- W4288302912 hasAuthorship W4288302912A5064320583 @default.
- W4288302912 hasBestOaLocation W42883029121 @default.
- W4288302912 hasConcept C102519508 @default.
- W4288302912 hasConcept C114614502 @default.
- W4288302912 hasConcept C115624301 @default.
- W4288302912 hasConcept C115961682 @default.
- W4288302912 hasConcept C119857082 @default.
- W4288302912 hasConcept C121332964 @default.
- W4288302912 hasConcept C134306372 @default.
- W4288302912 hasConcept C136119220 @default.
- W4288302912 hasConcept C154945302 @default.
- W4288302912 hasConcept C179415260 @default.
- W4288302912 hasConcept C185592680 @default.
- W4288302912 hasConcept C190470478 @default.
- W4288302912 hasConcept C202444582 @default.
- W4288302912 hasConcept C203436722 @default.
- W4288302912 hasConcept C2781311116 @default.
- W4288302912 hasConcept C33923547 @default.
- W4288302912 hasConcept C37914503 @default.
- W4288302912 hasConcept C41008148 @default.
- W4288302912 hasConcept C45347329 @default.
- W4288302912 hasConcept C50644808 @default.
- W4288302912 hasConcept C62520636 @default.
- W4288302912 hasConcept C67996461 @default.
- W4288302912 hasConcept C8010536 @default.
- W4288302912 hasConcept C81651864 @default.
- W4288302912 hasConceptScore W4288302912C102519508 @default.
- W4288302912 hasConceptScore W4288302912C114614502 @default.
- W4288302912 hasConceptScore W4288302912C115624301 @default.
- W4288302912 hasConceptScore W4288302912C115961682 @default.
- W4288302912 hasConceptScore W4288302912C119857082 @default.
- W4288302912 hasConceptScore W4288302912C121332964 @default.
- W4288302912 hasConceptScore W4288302912C134306372 @default.
- W4288302912 hasConceptScore W4288302912C136119220 @default.
- W4288302912 hasConceptScore W4288302912C154945302 @default.
- W4288302912 hasConceptScore W4288302912C179415260 @default.
- W4288302912 hasConceptScore W4288302912C185592680 @default.
- W4288302912 hasConceptScore W4288302912C190470478 @default.
- W4288302912 hasConceptScore W4288302912C202444582 @default.
- W4288302912 hasConceptScore W4288302912C203436722 @default.
- W4288302912 hasConceptScore W4288302912C2781311116 @default.
- W4288302912 hasConceptScore W4288302912C33923547 @default.
- W4288302912 hasConceptScore W4288302912C37914503 @default.
- W4288302912 hasConceptScore W4288302912C41008148 @default.
- W4288302912 hasConceptScore W4288302912C45347329 @default.
- W4288302912 hasConceptScore W4288302912C50644808 @default.
- W4288302912 hasConceptScore W4288302912C62520636 @default.
- W4288302912 hasConceptScore W4288302912C67996461 @default.
- W4288302912 hasConceptScore W4288302912C8010536 @default.
- W4288302912 hasConceptScore W4288302912C81651864 @default.
- W4288302912 hasLocation W42883029121 @default.
- W4288302912 hasOpenAccess W4288302912 @default.
- W4288302912 hasPrimaryLocation W42883029121 @default.
- W4288302912 hasRelatedWork W1483026439 @default.
- W4288302912 hasRelatedWork W1967762078 @default.
- W4288302912 hasRelatedWork W2019579972 @default.
- W4288302912 hasRelatedWork W2023264675 @default.
- W4288302912 hasRelatedWork W2037868132 @default.
- W4288302912 hasRelatedWork W2054069865 @default.
- W4288302912 hasRelatedWork W2118404717 @default.
- W4288302912 hasRelatedWork W2324427578 @default.
- W4288302912 hasRelatedWork W2971981099 @default.
- W4288302912 hasRelatedWork W4288302912 @default.
- W4288302912 isParatext "false" @default.
- W4288302912 isRetracted "false" @default.
- W4288302912 workType "article" @default.