Linear Operators: Spectral operators |
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Page 1930
... plane which contains the void set and the whole plane , in short , if Σ is a field of sets in the complex plane , then a spectral measure E on Σ is called a resolution of the identity ( or a spectral resolution ) for the operator T if E ...
... plane which contains the void set and the whole plane , in short , if Σ is a field of sets in the complex plane , then a spectral measure E on Σ is called a resolution of the identity ( or a spectral resolution ) for the operator T if E ...
Page 2043
... plane in the imaginary axis also hold . PROOF . We shall first need a bound for the norm of the analytic extension T1 ( ) of the semi - group T ( t ) to the half plane R ( 5 ) > 0 . Let R ( ) > 0 so that I eto with π / 20 / 2 . Then ...
... plane in the imaginary axis also hold . PROOF . We shall first need a bound for the norm of the analytic extension T1 ( ) of the semi - group T ( t ) to the half plane R ( 5 ) > 0 . Let R ( ) > 0 so that I eto with π / 20 / 2 . Then ...
Page 2087
... plane R ( S ) > 0 . For every ( 0 ) in Ho there is one and only one continuous map t → q ( t ) of [ 0 , ∞ ) into 5 " which is differentiable for t > 0 and has the properties ( ii ) ( iii ) ( iv ) p ( t ) e ( p ) T ( 24 ) ( RN ) , q ...
... plane R ( S ) > 0 . For every ( 0 ) in Ho there is one and only one continuous map t → q ( t ) of [ 0 , ∞ ) into 5 " which is differentiable for t > 0 and has the properties ( ii ) ( iii ) ( iv ) p ( t ) e ( p ) T ( 24 ) ( RN ) , q ...
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