Linear Operators: Spectral operators |
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Page 1933
... resolvent of a bounded spectral operator have a number of important properties not enjoyed by functions of the form R ( § ; T ) x when T is not a spectral operator ... RESOLVENT OF A SPECTRAL OPERATOR The Resolvent of a Spectral Operator.
... resolvent of a bounded spectral operator have a number of important properties not enjoyed by functions of the form R ( § ; T ) x when T is not a spectral operator ... RESOLVENT OF A SPECTRAL OPERATOR The Resolvent of a Spectral Operator.
Page 2291
... resolvent occurs so frequently in this section , it will be convenient to introduce , in the following definition , a special term for such operators . 1 DEFINITION . An operator T is discrete if there is a number in its resolvent set ...
... resolvent occurs so frequently in this section , it will be convenient to introduce , in the following definition , a special term for such operators . 1 DEFINITION . An operator T is discrete if there is a number in its resolvent set ...
Page 2316
... resolvent . By Lemma 8 , the condition for this is ( ❤n , n ) = 0 , where n is a solution of ( T * − √n 1 * ) & n = 0 . - Since by Theorems XIII.2.10 and XII.4.28 , T * is defined by the formal differential operator — ( d / dt ) 2 ...
... resolvent . By Lemma 8 , the condition for this is ( ❤n , n ) = 0 , where n is a solution of ( T * − √n 1 * ) & n = 0 . - Since by Theorems XIII.2.10 and XII.4.28 , T * is defined by the formal differential operator — ( d / dt ) 2 ...
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