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 f 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 f 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  , it holds for all â in  ... 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  , it holds for all â in  ... 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 = lim „ T2 to mean that ( iv ) Tq = lim T29 , n φε Φ . 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 of ...
... set , then we define T = lim „ T2 to mean that ( iv ) Tq = lim T29 , n φε Φ . 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 of ...
Contents
SPECTRAL OPERATORS | 1924 |
An Operational Calculus for Bounded Spectral | 1941 |
Bounded Spectral Operators in Hilbert Space | 1947 |
Copyright | |
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A₁ Acad adjoint operator algebra of projections Amer analytic arbitrary B-algebra B-space 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 dense differential operator Dokl Doklady Akad eigenvalues elements equation exists formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis ibid identity inequality inverse Krein L₁ Lemma locally convex spaces multiplicity Nauk SSSR norm normal operators operators in Hilbert perturbation polynomial Proc PROOF properties prove Pure Appl quasi-nilpotent resolution Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose topology trace class type spectral operator unbounded uniformly bounded vector zero