SPECTRAL THEORY AND FUNCTIONAL-CALCULUS FOR OPERATORS ON SPACES OF GENERALIZED-FUNCTIONS

被引：5

作者：

LAMB, W

MCGHEE, DF

机构：

[1] Department of Mathematics, University of Strathclyde, Glasgow, Scotland

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 1992年 / 163卷 / 01期

关键词：

D O I：

10.1016/0022-247X(92)90291-K

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The generalized eigenfunction expansion theory of Zemanian for a differential operator with discrete spectrum is extended to an arbitrary self-adjoint operator on a separable Hilbert space. The extension of the operator to an appropriately defined space of distributions is shown to have a spectral resolution in that space and a functional calculus is developed. Applications to the solution of distributional initial-boundary value problems via semigroup theory are considered. © 1992.

引用

页码：238 / 260

页数：23

共 10 条

[1]

Folland G.B., 1976, INTRO PARTIAL DIFFER

[2]

GELFAND IM, 1967, GENERALIZED FUNCTION, V3

[3]

Hille E., 1957, FUNCTIONAL ANAL SEMI

[4] ZEMANIANS DISTRIBUTIONAL EIGENFUNCTION TRANSFORMS [J].