Spectral Properties of Noncommuting Operators
Jefferies, Brian.
Spectral Properties of Noncommuting Operators [electronic resource] / by Brian Jefferies. - VII, 184 p. online resource. - Lecture Notes in Mathematics, 1843 0075-8434 ; . - Lecture Notes in Mathematics, 1843 .
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.
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.
9783540707462
10.1007/b97327 doi
Global analysis (Mathematics).
Operator theory.
Functions of complex variables.
Fourier analysis.
Analysis.
Operator Theory.
Functions of a Complex Variable.
Fourier Analysis.
QA299.6-433
515
Spectral Properties of Noncommuting Operators [electronic resource] / by Brian Jefferies. - VII, 184 p. online resource. - Lecture Notes in Mathematics, 1843 0075-8434 ; . - Lecture Notes in Mathematics, 1843 .
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.
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.
9783540707462
10.1007/b97327 doi
Global analysis (Mathematics).
Operator theory.
Functions of complex variables.
Fourier analysis.
Analysis.
Operator Theory.
Functions of a Complex Variable.
Fourier Analysis.
QA299.6-433
515