Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |
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Page 2373
... eigenfunction expansion theory of these intermediate cases is the subject of Steven P. Hoffman , Jr. [ 1 ] . B. Friedman and L. I. Mishoe [ 1 ] studied expansions in terms of the eigenfunctions of the equation u ” + q ( t ) u + λ ( p ...
... eigenfunction expansion theory of these intermediate cases is the subject of Steven P. Hoffman , Jr. [ 1 ] . B. Friedman and L. I. Mishoe [ 1 ] studied expansions in terms of the eigenfunctions of the equation u ” + q ( t ) u + λ ( p ...
Page 2374
... EIGENFUNCTION EXPANSIONS . The question of the expansion of a given function in terms of eigenfunctions ( or generalized eigenfunctions ) of an operator has been discussed by many authors . In addition , it is desirable to know when the ...
... EIGENFUNCTION EXPANSIONS . The question of the expansion of a given function in terms of eigenfunctions ( or generalized eigenfunctions ) of an operator has been discussed by many authors . In addition , it is desirable to know when the ...
Page 2538
... Eigenfunction expansions associated with the Schrödinger operators and their applications to scattering theory ... eigenfunctions for the exterior problem connected with −4 . Arch . Rat . Mech . Anal . 19 , 71-73 ( 1965 ) . 4 . On ...
... Eigenfunction expansions associated with the Schrödinger operators and their applications to scattering theory ... eigenfunctions for the exterior problem connected with −4 . Arch . Rat . Mech . Anal . 19 , 71-73 ( 1965 ) . 4 . On ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
Copyright | |
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Common terms and phrases
A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions 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 E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem 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