Linear Operators: Spectral operators |
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Page 2118
... operator T defined by ( Tf ) ( t ) = tf ( t ) , t € [ 0 , 1 ] , is a generalized scalar operator with spectral distribution ( U ( q ) f ) ( t ) = q ( t ) f ( t ) for 9 € C ° . It is proved ( see Foiaş [ 9 ] or 2118 XV.16 XV . SPECTRAL ...
... operator T defined by ( Tf ) ( t ) = tf ( t ) , t € [ 0 , 1 ] , is a generalized scalar operator with spectral distribution ( U ( q ) f ) ( t ) = q ( t ) f ( t ) for 9 € C ° . It is proved ( see Foiaş [ 9 ] or 2118 XV.16 XV . SPECTRAL ...
Page 2120
... spectral function if ( i ) the map f → U , is an alge- braic homomorphism with U。= I , and ( ii ) the map έ → U12 of N into B ( X ) is analytic on the complement of the support of ... operator and N is a 2120 XV.16 XV . SPECTRAL OPERATORS.
... spectral function if ( i ) the map f → U , is an alge- braic homomorphism with U。= I , and ( ii ) the map έ → U12 of N into B ( X ) is analytic on the complement of the support of ... operator and N is a 2120 XV.16 XV . SPECTRAL OPERATORS.
Page 2590
... operator , definition of , XV.4.2 ( 1938 ) spectrum of , XV.4.3 ( 1939 ) Quasi - nilpotent part of a spectral opera- tor , definition of , XV.4.6 ( 1941 ) Radical part of a spectral operator , defini- tion of , XV.4.6 ( 1941 ) Range of a ...
... operator , definition of , XV.4.2 ( 1938 ) spectrum of , XV.4.3 ( 1939 ) Quasi - nilpotent part of a spectral opera- tor , definition of , XV.4.6 ( 1941 ) Radical part of a spectral operator , defini- tion of , XV.4.6 ( 1941 ) Range of a ...
Contents
SPECTRAL OPERATORS | 1924 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
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A₁ 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 operator 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 subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero