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 |
From inside the book
Results 1-3 of 86
Page 2066
... function f in L1 for which h ( f ) # 0 and , in terms of the translation ft ( s ) = f ( s — t ) , define the complex valued function 1 ( 8 ) c ( t ) h ( ft ) h ( f ) tЄ RN . Since f * g = g , * f for every pair of functions f , g in L1 ...
... function f in L1 for which h ( f ) # 0 and , in terms of the translation ft ( s ) = f ( s — t ) , define the complex valued function 1 ( 8 ) c ( t ) h ( ft ) h ( f ) tЄ RN . Since f * g = g , * f for every pair of functions f , g in L1 ...
Page 2189
... ( f ) S ( g ) if ƒ and g are characteristic functions of sets in 2. For a fixed characteristic function f the set of g in EB ( A , E ) for which ( ii ) holds is linear ; and , in view of ( i ) , it is closed . Thus , since it contains all ...
... ( f ) S ( g ) if ƒ and g are characteristic functions of sets in 2. For a fixed characteristic function f the set of g in EB ( A , E ) for which ( ii ) holds is linear ; and , in view of ( i ) , it is closed . Thus , since it contains all ...
Page 2262
... { f } , then it follows from ( 4 ) that it holds for the limit function - 0 f = lim fn . n → ∞ Hence ( 5 ) holds if ƒ is any bounded Borel function vanishing at λ = 0 and at λ = v1 . A repetition of this argument shows that ( 5 ) still ...
... { f } , then it follows from ( 4 ) that it holds for the limit function - 0 f = lim fn . n → ∞ Hence ( 5 ) holds if ƒ is any bounded Borel function vanishing at λ = 0 and at λ = v1 . A repetition of this argument shows that ( 5 ) still ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
Copyright | |
23 other sections not shown
Other editions - View all
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