Linear Operators, Part 2 |
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Page 1955
... spectrum , and the spectral points of an operator in X will be classified , as they were in Hilbert space , according to the following definition . -- 1 DEFINITION . Let ... SPECTRUM OF A SPECTRAL OPERATOR The Spectrum of a Spectral Operator.
... spectrum , and the spectral points of an operator in X will be classified , as they were in Hilbert space , according to the following definition . -- 1 DEFINITION . Let ... SPECTRUM OF A SPECTRAL OPERATOR The Spectrum of a Spectral Operator.
Page 2507
... spectrum of H can change drastically . In particular , the " absolutely continuous spectrum " o ( H | Σac ( h ) ) ( cf. Definition 4.7 ) can disappear , grow , or be shifted . The study of these phenomena is of great interest in ...
... spectrum of H can change drastically . In particular , the " absolutely continuous spectrum " o ( H | Σac ( h ) ) ( cf. Definition 4.7 ) can disappear , grow , or be shifted . The study of these phenomena is of great interest in ...
Page 2591
... Spectrum , of a spectral operator , XV.8 ( 1954 ) condition to be in point spectrum , XV.15.13 ( 2076 ) continuous spectrum , definition of , XV.8.1 ( 1955 ) examples of , XV.15.37 , XV.15.38 , XV.15.39 ( 2080 ) point spectrum ...
... Spectrum , of a spectral operator , XV.8 ( 1954 ) condition to be in point spectrum , XV.15.13 ( 2076 ) continuous spectrum , definition of , XV.8.1 ( 1955 ) examples of , XV.15.37 , XV.15.38 , XV.15.39 ( 2080 ) point spectrum ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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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 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