Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |
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Page 1990
... function ƒ on RN or a complex valued set function defined on a family ( A ) of sets in RN . The representation ( 18 ) or ( 19 ) of a given convolution operator depends upon the interpreta- tion of the integral , that is , whether the ...
... function ƒ on RN or a complex valued set function defined on a family ( A ) of sets in RN . The representation ( 18 ) or ( 19 ) of a given convolution operator depends upon the interpreta- tion of the integral , that is , whether the ...
Page 2030
... functions , then these two functions coincide almost everywhere on RN . PROOF . For any given compact set K there is a function in Ø for which q ( s ) = 1 on K ( XIV.2.1 ) . It follows that any function which deter- mines a tempered ...
... functions , then these two functions coincide almost everywhere on RN . PROOF . For any given compact set K there is a function in Ø for which q ( s ) = 1 on K ( XIV.2.1 ) . It follows that any function which deter- mines a tempered ...
Page 2169
... functions , it follows that this map is also a homomorphism on the algebra of continuous functions . To see that it is a homomorphism on the algebra of bounded Borel functions , note that for a fixed continuous function g the set of all ...
... functions , it follows that this map is also a homomorphism on the algebra of continuous functions . To see that it is a homomorphism on the algebra of bounded Borel functions , note that for a fixed continuous function g the set of all ...
Contents
SPECTRAL OPERATORS | 1924 |
The Resolvent of a Spectral Operator | 1935 |
An Operational Calculus for Bounded Spectral | 1941 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial PROOF properties prove quasi-nilpotent resolution Russian S₁ satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset subspace Suppose trace class type spectral operator unbounded uniformly bounded unique vector zero