Spectral Properties of Noncommuting Operators (Lecture Notes in Mathematics Vol.1843) （2004. VIII, 184 p.）

Jefferies, B. R.

SPRINGER, BERLIN（2004発売）

SPRINGER, BERLIN（2004発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 184 p.
• 商品コード 9783540219231

Full Description

Forming functions of operators is a basic task of many areas of linear analysis and quantum physics. Weyl's functional calculus, initially applied to the position and momentum operators of quantum mechanics, also makes sense for finite systems of selfadjoint operators. By using the Cauchy integral formula available from Clifford analysis, the book examines how functions of a finite collection of operators can be formed when the Weyl calculus is not defined. The technique is applied to the determination of the support of the fundamental solution of a symmetric hyperbolic system of partial differential equations and to proving the boundedness of the Cauchy integral operator on a Lipschitz surface.

Contents

Introduction.- Weyl Calculus.- Clifford Analysis.- Functional Calculus for Noncommuting Operators.- The Joint Spectrum of Matrices.- The Monogenic Calculus for Sectorial Operators.- Feynman's Operational Calculus.- References.- Index.