Linear Operators: Spectral operators |
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Page 1930
... complex plane which contains the void set and the whole plane , in short , if Σ is a field of sets in the complex plane , then a spectral measure E on Σ is called a resolution of the identity ( or a spectral resolution ) for the ...
... complex plane which contains the void set and the whole plane , in short , if Σ is a field of sets in the complex plane , then a spectral measure E on Σ is called a resolution of the identity ( or a spectral resolution ) for the ...
Page 2188
... complex B - space X which is defined and countably additive on a o - field Σ of subsets of a set △ and let g be a bounded Borel measurable function defined on the complex plane . Then √ g ( f ( x ) ) E ( d ) ) = √ , 9 ( μ ) E ( ƒ ...
... complex B - space X which is defined and countably additive on a o - field Σ of subsets of a set △ and let g be a bounded Borel measurable function defined on the complex plane . Then √ g ( f ( x ) ) E ( d ) ) = √ , 9 ( μ ) E ( ƒ ...
Page 2335
... complex number . If λ is in the right half - plane , let μμ ( A ) denote that unique nth root of A which lies in the angular sector { μ | π / 2n≥ arg μ > —π / 2n } . If λ is in the left half - plane , let μ ( λ ) denote that unique nth ...
... complex number . If λ is in the right half - plane , let μμ ( A ) denote that unique nth root of A which lies in the angular sector { μ | π / 2n≥ arg μ > —π / 2n } . If λ is in the left half - plane , let μ ( λ ) denote that unique nth ...
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