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