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 ( S ) > 0 so that = | S | et with —π / 2 < 0 < π / 2 . Then since ...
... 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 ( S ) > 0 so that = | S | et with —π / 2 < 0 < π / 2 . Then since ...
Page 2087
... plane R ( ) > 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 ( ) > 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 adjoint operator algebra of projections Amer analytic arbitrary B-algebra B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded Borel function bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain eigenvalues elements equation exists finite number follows from Lemma follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial PROOF properties prove quasi-nilpotent resolution Russian S₁ satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset subspace Suppose trace class type spectral operator unbounded uniformly bounded unique vector zero