Linear Operators: Spectral operators |
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Page 2292
... corresponding to the eigenvalue λo . If E ( λo ; T ) = E ( o ) is the idempotent function of T corresponding to the analytic function which is one near λ and zero elsewhere near the spectrum of T and near infinity , then E ( λ ...
... corresponding to the eigenvalue λo . If E ( λo ; T ) = E ( o ) is the idempotent function of T corresponding to the analytic function which is one near λ and zero elsewhere near the spectrum of T and near infinity , then E ( λ ...
Page 2305
... corresponding to these eigen- values is one - dimensional . It follows immediately from Corollary 9 that L + B is a ... corresponding eigenfunctions ( the corresponding projections having one- dimensional ranges ) are e2ninx , n = 0 ...
... corresponding to these eigen- values is one - dimensional . It follows immediately from Corollary 9 that L + B is a ... corresponding eigenfunctions ( the corresponding projections having one- dimensional ranges ) are e2ninx , n = 0 ...
Page 2507
... corresponding to a two- body force in a three - body system ) , then the spectrum of H + V consists of the purely continuous spectrum corresponding to the spectrum of H , a point spectrum corresponding to the " bound states " of the ...
... corresponding to a two- body force in a three - body system ) , then the spectrum of H + V consists of the purely continuous spectrum corresponding to the spectrum of H , a point spectrum corresponding to the " bound states " of 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