Matches in SemOpenAlex for { <https://semopenalex.org/work/W1515665034> ?p ?o ?g. }
Showing items 1 to 71 of
71
with 100 items per page.
- W1515665034 abstract "We develop a group-theoretic method to generalize the Laplace-Beltrami operators on the classical domains. In K. Okamoto, Harmonic analysis on homogeneous vector bundles, Lecture Notes in Mathematics, Springer-Verlag, 266 (1971), 255–271, inspired by Helgason's paper, A duality for symmetric spaces with applications to group representations, Advan. Math. 5 (1970), 1–154, we defined the Poisson transforms for homogeneous vector bundles over symmetric spaces. In K. Okamoto, M. Tsukamoto and K. Yokota, Generalized Poisson and Cauchy kernel functions on classical domains, Japan. J. Math. 26 No. 1 (2000), 51–103., we defined the generalized Poisson-Cauchy transforms for homogeneous holomorphic line bundles over hermitian symmetric spaces and computed explicitly the kernel functions for each type of the classical domains. In E. Imamura, K. Okamoto, M. Tsukamoto and A. Yamamori, Generalized Laplacians for Generalized Poisson-Cauchy transforms on classical domains, Proc. Japan Acad., 82, Ser. A (2006), 167–172., making use of the Casimir operator, we defined the generalized Laplacians on homogeneous holomorphic line bundles over hermitian symmetric spaces and showed that the generalized Poisson-Cauchy transforms give rise to eigenfunctions of the generalized Laplacians. In this paper, using the canonical coordinates for each type of the classical domains, we carry out the direct computation to obtain the explicit formulas of (line bundle valued) invariant differential operators which we call the generalized Laplacians and compute their eigenvalues evaluated at the generalized Poisson-Cauchy kernel functions" @default.
- W1515665034 created "2016-06-24" @default.
- W1515665034 creator A5017773306 @default.
- W1515665034 creator A5033109052 @default.
- W1515665034 creator A5059271363 @default.
- W1515665034 creator A5069363313 @default.
- W1515665034 date "2009-07-01" @default.
- W1515665034 modified "2023-09-26" @default.
- W1515665034 title "Eigenvalues of generalized Laplacians for generalized Poisson-Cauchy transforms on classical domains" @default.
- W1515665034 cites W148098240 @default.
- W1515665034 cites W1515073151 @default.
- W1515665034 cites W1527329021 @default.
- W1515665034 cites W1566375981 @default.
- W1515665034 cites W1744403141 @default.
- W1515665034 cites W2033112001 @default.
- W1515665034 cites W2066038589 @default.
- W1515665034 cites W2077652184 @default.
- W1515665034 cites W2087640086 @default.
- W1515665034 cites W2333498920 @default.
- W1515665034 doi "https://doi.org/10.32917/hmj/1249046339" @default.
- W1515665034 hasPublicationYear "2009" @default.
- W1515665034 type Work @default.
- W1515665034 sameAs 1515665034 @default.
- W1515665034 citedByCount "4" @default.
- W1515665034 countsByYear W15156650342013 @default.
- W1515665034 countsByYear W15156650342019 @default.
- W1515665034 countsByYear W15156650342021 @default.
- W1515665034 crossrefType "journal-article" @default.
- W1515665034 hasAuthorship W1515665034A5017773306 @default.
- W1515665034 hasAuthorship W1515665034A5033109052 @default.
- W1515665034 hasAuthorship W1515665034A5059271363 @default.
- W1515665034 hasAuthorship W1515665034A5069363313 @default.
- W1515665034 hasBestOaLocation W15156650341 @default.
- W1515665034 hasConcept C134306372 @default.
- W1515665034 hasConcept C202444582 @default.
- W1515665034 hasConcept C204575570 @default.
- W1515665034 hasConcept C33923547 @default.
- W1515665034 hasConcept C49344536 @default.
- W1515665034 hasConcept C69151251 @default.
- W1515665034 hasConcept C8077415 @default.
- W1515665034 hasConcept C94940 @default.
- W1515665034 hasConcept C95857938 @default.
- W1515665034 hasConceptScore W1515665034C134306372 @default.
- W1515665034 hasConceptScore W1515665034C202444582 @default.
- W1515665034 hasConceptScore W1515665034C204575570 @default.
- W1515665034 hasConceptScore W1515665034C33923547 @default.
- W1515665034 hasConceptScore W1515665034C49344536 @default.
- W1515665034 hasConceptScore W1515665034C69151251 @default.
- W1515665034 hasConceptScore W1515665034C8077415 @default.
- W1515665034 hasConceptScore W1515665034C94940 @default.
- W1515665034 hasConceptScore W1515665034C95857938 @default.
- W1515665034 hasIssue "2" @default.
- W1515665034 hasLocation W15156650341 @default.
- W1515665034 hasLocation W15156650342 @default.
- W1515665034 hasOpenAccess W1515665034 @default.
- W1515665034 hasPrimaryLocation W15156650341 @default.
- W1515665034 hasRelatedWork W1949698423 @default.
- W1515665034 hasRelatedWork W2587330424 @default.
- W1515665034 hasRelatedWork W2788156798 @default.
- W1515665034 hasRelatedWork W2985874623 @default.
- W1515665034 hasRelatedWork W3015808232 @default.
- W1515665034 hasRelatedWork W3099040097 @default.
- W1515665034 hasRelatedWork W4200304030 @default.
- W1515665034 hasRelatedWork W4206268313 @default.
- W1515665034 hasRelatedWork W4221142480 @default.
- W1515665034 hasRelatedWork W4287815365 @default.
- W1515665034 hasVolume "39" @default.
- W1515665034 isParatext "false" @default.
- W1515665034 isRetracted "false" @default.
- W1515665034 magId "1515665034" @default.
- W1515665034 workType "article" @default.