Continuous and discrete tight frames of orthogonal polynomials for a radially symmetric weight

Show simple item record

dc.contributor.author Waldron, Shayne en
dc.date.accessioned 2012-04-03T02:29:41Z en
dc.date.issued 2009 en
dc.identifier.citation Constructive Approximation 30(1):33-52 2009 en
dc.identifier.issn 0176-4276 en
dc.identifier.uri http://hdl.handle.net/2292/16554 en
dc.description.abstract This paper considers tight frame decompositions of the Hilbert space Pn of orthogonal polynomials of degree n for a radially symmetric weight on Rd , e.g., the multivariate Gegenbauer and Hermite polynomials. We explicitly construct a single zonal polynomial p ∈ Pn with the property that each f ∈ Pn can be reconstructed as a sum of its projections onto the orbit of p under SO(d) (symmetries of the weight), and hence of its projections onto the zonal polynomials pξ obtained from p by moving its pole to ξ ∈ S := {ξ ∈ Rd : |ξ| = 1}. Furthermore, discrete versions of these integral decompositions also hold where SO(d) is replaced by a suitable finite subgroup, and S by a suitable finite subset. One consequence of our decomposition is a simple closed form for the reproducing kernel for Pn. en
dc.publisher Springer Verlag en
dc.relation.ispartofseries Constructive Approximation en
dc.rights Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. Details obtained form: http://www.sherpa.ac.uk/romeo/issn/0176-4276/ en
dc.rights.uri https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm en
dc.title Continuous and discrete tight frames of orthogonal polynomials for a radially symmetric weight en
dc.type Journal Article en
dc.identifier.doi 10.1007/s00365-008-9021-3 en
pubs.issue 1 en
pubs.begin-page 33 en
pubs.volume 30 en
dc.rights.holder Copyright: Springer Verlag en
pubs.end-page 52 en
dc.rights.accessrights http://purl.org/eprint/accessRights/RestrictedAccess en
pubs.subtype Article en
pubs.elements-id 78774 en
pubs.org-id Science en
pubs.org-id Mathematics en
pubs.record-created-at-source-date 2010-09-01 en


Files in this item

There are no files associated with this item.

Find Full text

This item appears in the following Collection(s)

Show simple item record

Share

Search ResearchSpace


Browse

Statistics