Linear Operators: Spectral operators |
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Page 2219
... finite number of Jordan arcs , no two of which intersect in more than a finite number of points , then V has the required property . α PROOF . Since the operators T , are scalar XVII.4.1 2219 STRONG LIMITS OF SPECTRAL OPERATORS.
... finite number of Jordan arcs , no two of which intersect in more than a finite number of points , then V has the required property . α PROOF . Since the operators T , are scalar XVII.4.1 2219 STRONG LIMITS OF SPECTRAL OPERATORS.
Page 2338
... finite number of the roots of M ( μ ) = 0 which lie in A , are simple , and that they may be enumerated in a sequence έm in such a way that we have an asymptotic expression ( 49 ) Em 1 + Σ m- " ) . ~ 2mm ( 1 + Σ c2m - n n = 1 The ...
... finite number of the roots of M ( μ ) = 0 which lie in A , are simple , and that they may be enumerated in a sequence έm in such a way that we have an asymptotic expression ( 49 ) Em 1 + Σ m- " ) . ~ 2mm ( 1 + Σ c2m - n n = 1 The ...
Page 2362
... finite number of the points in o ( 7 ) are simple poles of the resolvent function R ( λ ; T ) ; let { U1 } be a sequence of bounded domains covering the entire plane , such that lim , i minze U1 | 2 | Ui = ∞ . It is assumed that the ...
... finite number of the points in o ( 7 ) are simple poles of the resolvent function R ( λ ; T ) ; let { U1 } be a sequence of bounded domains covering the entire plane , such that lim , i minze U1 | 2 | Ui = ∞ . It is assumed that the ...
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