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.