Matches in SemOpenAlex for { <https://semopenalex.org/work/W2044095946> ?p ?o ?g. }
Showing items 1 to 80 of
80
with 100 items per page.
- W2044095946 endingPage "193" @default.
- W2044095946 startingPage "159" @default.
- W2044095946 abstract "Analysis on Lie groups and their homogeneous spaces has seen a recent flowering, thanks to the work of Harish-Chandra, Helgason, Selberg and many others. The purpose of this paper is to give an elementary discussion of Fourier analysis on the noneuclidean upper half plane H; that is, the spectral resolution of the noneuclidean Laplace operator $Delta $. This leads to a study of the elementary eigenfunctions of $Delta $. Such eigenfunctions can be viewed as analogues of the trigonometric functions in euclidean Fourier analysis. The elementary eigenfunctions of $Delta $ on H are Legendre (conical or spherical) functions, K-Bessel functions and Eisenstein series. The invariance of $Delta $ under the special linear group $G = SL(2,mathbb{R})$, of $2 times 2$ real matrices of determinant l, gives a way of recognizing the spectral measure in the noneuclidean Fourier inversion formula, once one knows the asymptotics and functional equations of the elementary eigenfunctions of $Delta $. In fact, this method allows a unified treatment of the inversion formulas for the standard integral transforms of mathematical physics. The connection between Fourier analysis on H and that on the fundamental domain $Gamma backslash H$, $Gamma = $ a discrete subgroup of G (e.g., $Gamma = $ the modular group $SL(2,mathbb{Z})$ of $2 times 2$ integer matrices of determinant 1) provides an analogue of the Poisson summation formula. Applications to the solution of the heat equation on H and $Gamma backslash H$ are considered, as well as the distribution of eigenvalues of the noneuclidean Laplacian on $L^2 (Gamma backslash H)$." @default.
- W2044095946 created "2016-06-24" @default.
- W2044095946 creator A5034686163 @default.
- W2044095946 date "1982-04-01" @default.
- W2044095946 modified "2023-09-24" @default.
- W2044095946 title "Noneuclidean Harmonic Analysis" @default.
- W2044095946 cites W153200967 @default.
- W2044095946 cites W1594206242 @default.
- W2044095946 cites W160837363 @default.
- W2044095946 cites W1974489250 @default.
- W2044095946 cites W1975356965 @default.
- W2044095946 cites W1976379494 @default.
- W2044095946 cites W2006332263 @default.
- W2044095946 cites W2049157349 @default.
- W2044095946 cites W2070302036 @default.
- W2044095946 cites W2072247311 @default.
- W2044095946 cites W2128633210 @default.
- W2044095946 cites W2328610912 @default.
- W2044095946 cites W2334519747 @default.
- W2044095946 cites W2491310912 @default.
- W2044095946 cites W2507077471 @default.
- W2044095946 cites W4231608385 @default.
- W2044095946 cites W4244148405 @default.
- W2044095946 cites W567544774 @default.
- W2044095946 doi "https://doi.org/10.1137/1024040" @default.
- W2044095946 hasPublicationYear "1982" @default.
- W2044095946 type Work @default.
- W2044095946 sameAs 2044095946 @default.
- W2044095946 citedByCount "14" @default.
- W2044095946 countsByYear W20440959462014 @default.
- W2044095946 countsByYear W20440959462019 @default.
- W2044095946 crossrefType "journal-article" @default.
- W2044095946 hasAuthorship W2044095946A5034686163 @default.
- W2044095946 hasConcept C102519508 @default.
- W2044095946 hasConcept C107706756 @default.
- W2044095946 hasConcept C121332964 @default.
- W2044095946 hasConcept C128803854 @default.
- W2044095946 hasConcept C134306372 @default.
- W2044095946 hasConcept C158693339 @default.
- W2044095946 hasConcept C165700671 @default.
- W2044095946 hasConcept C181633103 @default.
- W2044095946 hasConcept C187915474 @default.
- W2044095946 hasConcept C202444582 @default.
- W2044095946 hasConcept C33923547 @default.
- W2044095946 hasConcept C62520636 @default.
- W2044095946 hasConcept C64092710 @default.
- W2044095946 hasConceptScore W2044095946C102519508 @default.
- W2044095946 hasConceptScore W2044095946C107706756 @default.
- W2044095946 hasConceptScore W2044095946C121332964 @default.
- W2044095946 hasConceptScore W2044095946C128803854 @default.
- W2044095946 hasConceptScore W2044095946C134306372 @default.
- W2044095946 hasConceptScore W2044095946C158693339 @default.
- W2044095946 hasConceptScore W2044095946C165700671 @default.
- W2044095946 hasConceptScore W2044095946C181633103 @default.
- W2044095946 hasConceptScore W2044095946C187915474 @default.
- W2044095946 hasConceptScore W2044095946C202444582 @default.
- W2044095946 hasConceptScore W2044095946C33923547 @default.
- W2044095946 hasConceptScore W2044095946C62520636 @default.
- W2044095946 hasConceptScore W2044095946C64092710 @default.
- W2044095946 hasIssue "2" @default.
- W2044095946 hasLocation W20440959461 @default.
- W2044095946 hasOpenAccess W2044095946 @default.
- W2044095946 hasPrimaryLocation W20440959461 @default.
- W2044095946 hasRelatedWork W1501244378 @default.
- W2044095946 hasRelatedWork W1513846220 @default.
- W2044095946 hasRelatedWork W2044106429 @default.
- W2044095946 hasRelatedWork W2276419520 @default.
- W2044095946 hasRelatedWork W2334357536 @default.
- W2044095946 hasRelatedWork W2345384855 @default.
- W2044095946 hasRelatedWork W2383846213 @default.
- W2044095946 hasRelatedWork W4300860496 @default.
- W2044095946 hasRelatedWork W4302419125 @default.
- W2044095946 hasRelatedWork W1968923432 @default.
- W2044095946 hasVolume "24" @default.
- W2044095946 isParatext "false" @default.
- W2044095946 isRetracted "false" @default.
- W2044095946 magId "2044095946" @default.
- W2044095946 workType "article" @default.