Linear Operators, Part 2 |
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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  , it holds for all â in  ... function ዋ፡ with respect to the finitely additive set function A is the same as the integral of the numerical ...
... function of a set in Σ and , since linear combinations of such functions are dense in  , it holds for all â in  ... function ዋ፡ with respect to the finitely additive set function A is the same as the integral of the numerical ...
Page 2029
... set , then we define T = lim , T2 to mean that ( iv ) Tq = lim T2p , n φε Φ . 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 of ...
... set , then we define T = lim , T2 to mean that ( iv ) Tq = lim T2p , n φε Φ . 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 of ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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 Borel function 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 eigenvalues elements equation exists finite number follows from Lemma 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