Linear Operators: Spectral operators |
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Page 1990
... function â on RN . Before illustrating the results of the preceding section , we shall examine the structure of ... function f on RN or a complex valued set function à defined on a family ( A ) of sets in RN . The representation ( 18 ) ...
... function â on RN . Before illustrating the results of the preceding section , we shall examine the structure of ... function f on RN or a complex valued set function à defined on a family ( A ) of sets in RN . The representation ( 18 ) ...
Page 2030
... functions , then these two functions coincide almost everywhere on RN . PROOF . For any given compact set K there is a function in for which p ( 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 for which p ( s ) = 1 on K ( XIV.2.1 ) . It follows that any function which deter- mines a tempered ...
Page 2169
... 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 bounded Borel functions ƒ for which ( vi ) ( fg ) ( T ) = ƒ ( T ) g ( T ) , includes all ...
... 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 bounded Borel functions ƒ for which ( vi ) ( fg ) ( T ) = ƒ ( T ) g ( T ) , includes all ...
Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer arbitrary B*-algebra B₁ Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator Colojoară commuting compact complex numbers complex plane contains converges Corollary countably additive Definition dense differential operator disjoint Doklady Akad E-measurable eigenvalues elements equation equivalent exists Foias follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math matrix multiplicity norm operators in Hilbert perturbation polynomial PROOF proved quasi-nilpotent resolution restriction Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset subspace sufficiently type spectral operator unbounded unique vector weakly complete zero