Extensions of dissipative operators with closable imaginary part

Opuscula Mathematica

article

Christoph Fischbacher¹ 

[1] Department of Mathematics, University of California

关键词: extension theory;    dissipative operators;    ordinary differential operators.;   

DOI  :  10.7494/OpMath.2021.41.3.381

学科分类：环境科学（综合）

来源: AGH University of Science and Technology Press

【 摘 要 】

Given a dissipative operator \(A\) on a complex Hilbert space \(\mathcal{H}\) such that the quadratic form \(f \mapsto \text{Im}\langle f, Af \rangle\) is closable, we give a necessary and sufficient condition for an extension of \(A\) to still be dissipative. As applications, we describe all maximally accretive extensions of strictly positive symmetric operators and all maximally dissipative extensions of a highly singular first-order operator on the interval.

【 授权许可】

CC BY-NC