Linear Operators: Spectral operators |
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Page 1931
... analytic extension of R ( § ; T ) x will be meant an X - valued function ƒ defined and analytic on an open set D ( f ) p ( T ) and such that It is clear that , for such an extension , ( §I — T ) ƒ ( § ) = X , έe D ( f ) . έ = p ( T ) ...
... analytic extension of R ( § ; T ) x will be meant an X - valued function ƒ defined and analytic on an open set D ( f ) p ( T ) and such that It is clear that , for such an extension , ( §I — T ) ƒ ( § ) = X , έe D ( f ) . έ = p ( T ) ...
Page 1932
... analytic function with domain p ( x ) and with x ( ) = R ( ; T ) x , ξερ ( Τ ) . It will be shown in the next section that , if T is a spectral operator , the function R ( § ; T ) x has , for every x in X , the single valued extension ...
... analytic function with domain p ( x ) and with x ( ) = R ( ; T ) x , ξερ ( Τ ) . It will be shown in the next section that , if T is a spectral operator , the function R ( § ; T ) x has , for every x in X , the single valued extension ...
Page 2248
... analytic in a domain U which , when taken together with a finite number of exceptional points p , includes a ... analytic at infinity , then e1 = f - 1 ( e ) is bounded , and it follows from Theorem 9 ( ii ) that D ( f ( T ) ) E ( e1 ) X ...
... analytic in a domain U which , when taken together with a finite number of exceptional points p , includes a ... analytic at infinity , then e1 = f - 1 ( e ) is bounded , and it follows from Theorem 9 ( ii ) that D ( f ( T ) ) E ( e1 ) X ...
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