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 1990
... function ƒ on RN or a complex valued set function à defined on a family ( A ) of sets in RN . The representation ( 18 ) or ( 19 ) of a given convolution operator depends upon the interpreta- tion of the integral , that is , whether the ...
... function ƒ on RN or a complex valued set function à defined on a family ( A ) of sets in RN . The representation ( 18 ) or ( 19 ) of a given convolution operator depends upon the interpreta- tion of the integral , that is , whether the ...
Page 1993
... function of a set in Σ and , since linear combinations of such functions are dense in A , it holds for all â in A ... function 9 with respect to the finitely additive set function is the same as the integral of the numerical function X ...
... function of a set in Σ and , since linear combinations of such functions are dense in A , it holds for all â in A ... function 9 with respect to the finitely additive set function is the same as the integral of the numerical function X ...
Page 2029
... set , then we define T to mean that n = = lim2 Tn n ( iv ) Tq = lim T2q , n ΚΕΦ . n As an example of a tempered distribution we might mention the function T , determined by a bounded finitely additive set function v ( defined on some field ...
... set , then we define T to mean that n = = lim2 Tn n ( iv ) Tq = lim T2q , n ΚΕΦ . n As an example of a tempered distribution we might mention the function T , determined by a bounded finitely additive set function v ( defined on some field ...
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