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 ƒ 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 ƒ 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 p in Ø 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 p in Ø 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 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
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Common terms and phrases
A₁ adjoint operator algebra Amer analytic applications arbitrary B-space Banach Banach space Boolean algebra Borel sets boundary bounded Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding defined Definition denote dense determined differential operators Doklady Akad elements equation equivalent established example exists extension finite follows formula function given gives H₁ Hence Hilbert space hypothesis identity integral invariant inverse Lemma limit linear operators Math multiplicity Nauk SSSR norm normal perturbation plane positive preceding present problem Proc projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type sequence shown shows similar spectral measure spectral operator spectrum subset sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero