Show simple item record  

dc.contributor.authorKalnins, Ernie G.en_NZ
dc.contributor.authorMiller, W., Jr.en_NZ
dc.contributor.authorTratnik, M.V.en_NZ
dc.date.accessioned2018-11-08T02:39:27Z
dc.date.available1991-01-01en_NZ
dc.date.available2018-11-08T02:39:27Z
dc.date.issued1991en_NZ
dc.identifier.citationKalnins, E. G., Miller, W., Jr., & Tratnik, M. V. (1991). Families of Orthogonal and Biorthogonal Polynomials on the N-Sphere. SIAM Journal on Mathematical Analysis (SIMA), 22(1), 272–294. https://doi.org/10.1137/0522017en
dc.identifier.issn0036-1410en_NZ
dc.identifier.urihttps://hdl.handle.net/10289/12150
dc.description.abstractThe Laplace–Beltrami eigenvalue equation $H\Phi = \lambda \Phi $ on the n-sphere is studied, with an added vector potential term motivated by the differential equations for the polynomial Lauricella functions $F_A $. The operator H is self adjoint with respect to the natural inner product induced on the sphere and, in certain special coordinates, it admits a spectral decomposition with eigenspaces composed entirely of polynomials. The eigenvalues are degenerate but the degeneracy can be broken through use of the possible separable coordinate systems on the n-sphere. Then a basis for each eigenspace can be selected in terms of the simultaneous eigenfunctions of a family of commuting second-order differential operators that also commute with H. The results provide a multiplicity of n-variable orthogonal and biorthogonal families of polynomials that generalize classical results for one and two variable families of Jacobi polynomials on intervals, disks, and paraboloids.
dc.format.mimetypeapplication/pdf
dc.language.isoenen_NZ
dc.publisherSIAM PUBLICATIONSen_NZ
dc.rightsThis is an author’s accepted version of an article published in the journal: SIAM Journal on Mathematical Analysis (SIMA). © 1991 Society for Industrial and Applied Mathematics
dc.subjectScience & Technologyen_NZ
dc.subjectPhysical Sciencesen_NZ
dc.subjectMathematics, Applieden_NZ
dc.subjectMathematicsen_NZ
dc.subjectMULTIVARIABLE ORTHOGONAL AND BIORTHOGONAL POLYNOMIALSen_NZ
dc.subjectTHE N-SPHEREen_NZ
dc.titleFamilies of Orthogonal and Biorthogonal Polynomials on the N-Sphereen_NZ
dc.typeJournal Article
dc.identifier.doi10.1137/0522017en_NZ
dc.relation.isPartOfSIAM Journal on Mathematical Analysis (SIMA)en_NZ
pubs.begin-page272
pubs.elements-id191964
pubs.end-page294
pubs.issue1en_NZ
pubs.publication-statusPublisheden_NZ
pubs.volume22en_NZ


Files in this item

This item appears in the following Collection(s)

Show simple item record