## 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(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.

Original language | English (US) |
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Pages (from-to) | 367-372 |

Number of pages | 6 |

Journal | Proceedings of the American Mathematical Society |

Volume | 33 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1972 |

Externally published | Yes |

## Keywords

- Asymptotic distribution
- Eigenvalues
- Elliptic
- N-widths

## ASJC Scopus subject areas

- General Mathematics
- Applied Mathematics