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 ) ƒ ) ( t ) = q ( t ) f ( t ) for 9 € C1o . 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 ) ƒ ) ( t ) = q ( t ) f ( t ) for 9 € C1o . 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 → Uƒ¿ of Q into B ( X ) is analytic on the complement of the support ... 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 → Uƒ¿ of Q into B ( X ) is analytic on the complement of the support ... 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 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary asymptotic B₁ Banach space Boolean algebra Borel set boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complete Boolean algebra complex numbers complex plane continuous functions converges Corollary countably additive Definition denote differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem follows immediately formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality inverse L₁ Lebesgue Math multiplicity Nauk SSSR norm operators in Hilbert perturbation PROOF properties prove quasi-nilpotent resolution Russian satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose trace class type spectral operator unbounded uniformly bounded vector zero