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 2227
... Spectral Operators 1. Introduction It was shown in the course of Chapters XII , XIII , and XIV that in order to apply the spectral theory of Hermitian operators to ordinary and partial differential operators it is first necessary to ...
... Spectral Operators 1. Introduction It was shown in the course of Chapters XII , XIII , and XIV that in order to apply the spectral theory of Hermitian operators to ordinary and partial differential operators it is first necessary to ...
Page 2525
... theory of a class of non - self - adjoint operators and its applications to quantum scattering theory . Ann . Acad ... spectral operators . Proc . London Math . Soc . ( 3 ) 15 , 437-457 ( 1965 ) . 2. On some algebras of operators generated by ...
... theory of a class of non - self - adjoint operators and its applications to quantum scattering theory . Ann . Acad ... spectral operators . Proc . London Math . Soc . ( 3 ) 15 , 437-457 ( 1965 ) . 2. On some algebras of operators generated by ...
Page 2535
... spectral properties of normal operators . Acta Sci . Math . Szeged 12 Pars B , 153-156 ( 1950 ) . 6 . 11 . Introduction to Hilbert space and the theory of spectral multiplicity . Chelsea , New York , 1951 . Shifts on Hilbert spaces . J ...
... spectral properties of normal operators . Acta Sci . Math . Szeged 12 Pars B , 153-156 ( 1950 ) . 6 . 11 . Introduction to Hilbert space and the theory of spectral multiplicity . Chelsea , New York , 1951 . Shifts on Hilbert spaces . J ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
Copyright | |
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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