Linear Operators: Spectral operators |
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Page 2321
... denote the nth roots of unity , enumerated in such a way that wo = 1 , w , -1 , the imaginary part of w is positive for 0 < i < v , and the imaginary part of w , is negative for v < i < 2v . Let à be an arbitrary complex number . Let μ ...
... denote the nth roots of unity , enumerated in such a way that wo = 1 , w , -1 , the imaginary part of w is positive for 0 < i < v , and the imaginary part of w , is negative for v < i < 2v . Let à be an arbitrary complex number . Let μ ...
Page 2335
... denote the nth roots of unity , enumerated in such a way that w 。= 1 , the imaginary part of w is positive for 0 ... denote that unique nth root of λ which lies in the angular sector { μ / 2n arg μ > —π / 2n } . If A is in the left half ...
... denote the nth roots of unity , enumerated in such a way that w 。= 1 , the imaginary part of w is positive for 0 ... denote that unique nth root of λ which lies in the angular sector { μ / 2n arg μ > —π / 2n } . If A is in the left half ...
Page 2466
... denote the real axis , the Lebesgue measure on R , and v a finite positive λ - singular measure on R , so that there exists a A - null set e , such that v ( R − e , ) = 0 . Put μ = v + λ . Let ' denote the set of all sequences ƒ = { ƒ ...
... denote the real axis , the Lebesgue measure on R , and v a finite positive λ - singular measure on R , so that there exists a A - null set e , such that v ( R − e , ) = 0 . Put μ = v + λ . Let ' denote the set of all sequences ƒ = { ƒ ...
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