TY - JOUR

T1 - Asymptotic estimates of the «-widths in hilbert space

AU - Jerome, Joseph W.

N1 - Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.

PY - 1972/6

Y1 - 1972/6

N2 - 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(Ã¢r) 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 â€ž(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.

AB - 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(Ã¢r) 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 â€ž(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.

KW - Asymptotic distribution

KW - Eigenvalues

KW - Elliptic

KW - N-widths

UR - http://www.scopus.com/inward/record.url?scp=84966207538&partnerID=8YFLogxK

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U2 - 10.1090/S0002-9939-1972-0296583-8

DO - 10.1090/S0002-9939-1972-0296583-8

M3 - Article

AN - SCOPUS:84966207538

VL - 33

SP - 367

EP - 372

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 2

ER -