Functional Calculi

A Functional Calculus Is A Construction Which Associates With An Operator Or A Family Of Operators A Homomorphism From A Function Space Into A Subspace Of Continuous Linear Operators, I.e. A Method For Defining Oc Functions Of An Operatoroco. Perhaps The Most Familiar Example Is Based On The Spectral Theorem For Bounded Self-adjoint Operators On A Complex Hilbert Space.this Book Contains An Exposition Of Several Such Functional Calculi. In Particular, There Is An Exposition Based On The Spectral Theorem For Bounded, Self-adjoint Operators, An Extension To The Case Of Several Commuting Self-adjoint Operators And An Extension To Normal Operators. The Riesz Operational Calculus Based On The Cauchy Integral Theorem From Complex Analysis Is Also Described. Finally, An Exposition Of A Functional Calculus Due To H. Weyl Is Given. A functional calculus is a construction which associates with an operator or a family of operators a homomorphism from a function space into a subspace of continuous linear operators, i.e. a method for defining "functions of an operator". Perhaps the most familiar example is based on the spectral theorem for bounded self-adjoint operators on a complex Hilbert space. This book contains an exposition of several such functional calculi. In particular, there is an exposition based on the spectral theorem for bounded, self-adjoint operators, an extension to the case of several commuting self-adjoint operators and an extension to normal operators. The Riesz operational calculus based on the Cauchy integral theorem from complex analysis is also described. Finally, an exposition of a functional calculus due to H. Weyl is given -- Source other than Library of Congress A functional calculus is a construction which associates with an operator or a family of operators a homomorphism from a function space into a subspace of continuous linear operators, such as a method for defining "functions of an operator". This book contains an exposition of several such functional calculi.