Linear Operators: Spectral operators |
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Page 2010
... Unbounded Spectral Operators Although the topic of unbounded spectral operators will be treated in some detail in Chapter XVIII and many illustrations of such operators will be found in Chapters XIX and XX , we introduce the subject ...
... Unbounded Spectral Operators Although the topic of unbounded spectral operators will be treated in some detail in Chapter XVIII and many illustrations of such operators will be found in Chapters XIX and XX , we introduce the subject ...
Page 2013
... unbounded convolution . The preceding discussion may be summarized as follows . σ 2 THEOREM . For each measurable p × p matrix  ( s ) of complex functions defined almost everywhere on S and each measurable set o in S the operators  ...
... unbounded convolution . The preceding discussion may be summarized as follows . σ 2 THEOREM . For each measurable p × p matrix  ( s ) of complex functions defined almost everywhere on S and each measurable set o in S the operators  ...
Page 2227
... unbounded operators . The present chapter is an attempt to make the corresponding step in the theory of spectral operators . We ... Unbounded Spectral Operators 1 DEFINITION . Let denote the 2227 Unbounded Spectral Operators 1 Introduction.
... unbounded operators . The present chapter is an attempt to make the corresponding step in the theory of spectral operators . We ... Unbounded Spectral Operators 1 DEFINITION . Let denote the 2227 Unbounded Spectral Operators 1 Introduction.
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
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Common terms and phrases
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