Accession Number : AD0725589

Title :   Singular Quadratic Functionals,

Corporate Author : CALIFORNIA UNIV LOS ANGELES DEPT OF MATHEMATICS

Personal Author(s) : Stein,Junior

Report Date : 1971

Pagination or Media Count : 223

Abstract : The study of quadratic forms is an important part of variational theory. When a quadratic form that is an integral is nonsingular in the sense that a strengthened Legendre condition holds, then we can use an index theory of quadratic forms to obtain information about minimization problems, comparison and oscillation theorems for differential equations, the theory of conjugate and focal points, boundary value problems for differential equations and the Sturm Liouville theory for self-adjoint systems of differential equations, and the theory of eigenvalues. The index theory mentioned above is sometimes referred to as a local Morse theory. The purpose of this study is to see what can be said for each of these problems when the quadratic form is singular at only the endpoints. (Author)

Descriptors :   (*FUNCTIONAL ANALYSIS, THEOREMS), CALCULUS OF VARIATIONS, DIFFERENTIAL EQUATIONS, MATRICES(MATHEMATICS), TOPOLOGY, HILBERT SPACE, THESES

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE