Asymptotic estimates of the «-widths in hilbert space

Joseph W. Jerome*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Let fÃ-eRm be a bounded open set satisfying the restricted cone property and let R be a nonnegative selfadjoint operator on L2(fÃ) which is the realization of a uniformly elliptic operator A of order v with suitable coefficients and principal part a(x, (). Let St be the ellipsoid (f:(Rf, f)\). The Z.2 â-widths d(âr) satisfy ti,â(fM* where' c = J'â£2(Joa(I.f)i di) dx. If B(u, v) is a nonnegative Hermitian coercive form over a subspace f of the Sobolev space W:2(Q.), then the n-widths of.:#= (/e f:B(f, f)Sl] satisfy, 0(cT'"^h'm inf â „(Ã?)â*'"^ lim sup dn(J8)n::lmS(c")klm. In some cases c'=c=c" where c is defined in terms of an elliptic operator of order 2k. The â-widths of %i n WJ-2(fÃ), Q^jSk, are of order CKâ*-""â), noe.

Original languageEnglish (US)
Pages (from-to)367-372
Number of pages6
JournalProceedings of the American Mathematical Society
Volume33
Issue number2
DOIs
StatePublished - Jun 1972

Keywords

  • Asymptotic distribution
  • Eigenvalues
  • Elliptic
  • N-widths

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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