EXISTENCE OF MAXIMAL SEMIDEFINITE INVARIANT SUBSPACES AND SEMIGROUP PROPERTIES OF SOME CLASSES OF ORDINARY DIFFERENTIAL OPERATORS

被引：0

作者：

Pyatkov, S. G.

机构：

[1] 628012, Hanty-Mansiisk

来源：

OPERATORS AND MATRICES | 2014年 / 8卷 / 01期

关键词：

Dissipative operator; Krein space; invariant subspace; analytic semigroup; similarity; STURM-LIOUVILLE OPERATORS; SIMILARITY PROBLEM; SPECTRAL THEORY; INDEFINITE; INTERPOLATION;

D O I：

10.7153/oam-08-13

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We describe sufficient conditions for the operator Lu = 1/g(x)L(0)u, with L-o an ordinary differential operator dissipative on its domain and a function g changing its sign, to have maximal semidefinite invariant subspaces in the Krein space 122,8(a,b) with the indefinite inner product [u, v] = integral(b)(a) g(x)u(x)v(x) over bar dx. The semigroup properties of the restrictions of an operator to these subspaces are studied. The similarity problem of L to a selfadjoint operator is discussed.

引用

页码：237 / 254

页数：18

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