Linear Operators: Spectral operators |
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Page 2242
... Definition 10 , where ƒ ( z ) = z , then T is said to be an unbounded spectral operator of scalar type . The ... Definition 12 is a spectral operator in the sense of Definition 1. Moreover , the resolution of the identity for T in the ...
... Definition 10 , where ƒ ( z ) = z , then T is said to be an unbounded spectral operator of scalar type . The ... Definition 12 is a spectral operator in the sense of Definition 1. Moreover , the resolution of the identity for T in the ...
Page 2590
... 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 spectral ...
... 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 spectral ...
Page 2591
... definition of , XV.2.1 ( 1929 ) integral with respect to , XV.2 ( 1929 ) Spectral operator , adjoint of , XVI.4.6 ( 2148 ) , XVI.5.16 ( 2162 ) canonical reduction of , XV.4 ( 1937 ) , XV.4.5 ( 1939 ) , XVII.5.11 ( 2224 ) conditions for ...
... definition of , XV.2.1 ( 1929 ) integral with respect to , XV.2 ( 1929 ) Spectral operator , adjoint of , XVI.4.6 ( 2148 ) , XVI.5.16 ( 2162 ) canonical reduction of , XV.4 ( 1937 ) , XV.4.5 ( 1939 ) , XVII.5.11 ( 2224 ) conditions for ...
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