|
|||||
|
|
|
|
|
|
|
|
|
An approximation theory
for elliptic quadratic forms on Hilbert spaces: Application
to the eigenvalue problem for compact quadratic forms
John Gregory |
|
Vol. 37 (1971), No. 2, 383–395
|
Abstract |
|
A theory for an elliptic quadratic form J(x) defined on a Hilbert space A has been given by Hestenes. A fundamental part of this theory is concerned with the signature s and nullity n of J(χ) on A. These indices are used to develop a generalized Sturm-Lionville Theory and a Local Morse Theory. In this paper the theory of Hestenes is extended to elliptic quadratic forms J(x;σ) defined on A(σ) where σ is a member of the metric space (Σ,|0) and A(σ) denotes a closed subspace of A. A fundamental part of this extension is concerned with inequalities dealing with the signature s(σ) and nullity n(σ) of J(x;σ) on A(σ), where σ is in a ρ neighborhood of a fixed point σ0 in Σ. |
Mathematical Subject Classification
Primary: 46N05
Secondary: 49G99
|
Milestones
Received: 10 April 1970
Revised: 10 August 1970
Published: 1 May 1971
|
Authors |
| John Gregory | |
|
