Linear Operators: Spectral operators |
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Page 2285
... denoted by the single letter h . We shall define a map A of X into H. Let D ( A ) = { x | E „ x = D ( Aŋ ) for all n and Define Ex ... denote the range of the resolution of the identity E ( ) of Q and XVIII.3.35 2285 MULTIPLICITY THEORY.
... denoted by the single letter h . We shall define a map A of X into H. Let D ( A ) = { x | E „ x = D ( Aŋ ) for all n and Define Ex ... denote the range of the resolution of the identity E ( ) of Q and XVIII.3.35 2285 MULTIPLICITY THEORY.
Page 2436
... denotes the restriction of S to the subspace Co ( E " ) of D ( S ) , then So WT , W - 1 S. Se Let v denote the measure on E " defined by v ( e ) = √ . ( 1 + | x | * ) dx , so that by Theorem III.10.4 we have ( 13 ) ___ 90 ( x ) v ( dx ) ...
... denotes the restriction of S to the subspace Co ( E " ) of D ( S ) , then So WT , W - 1 S. Se Let v denote the measure on E " defined by v ( e ) = √ . ( 1 + | x | * ) dx , so that by Theorem III.10.4 we have ( 13 ) ___ 90 ( x ) v ( dx ) ...
Page 2466
... denote the real axis , the Lebesgue measure on R , and v a finite positive λ - singular measure on R , so that there exists a A - null set e , such that v ( R − e1 ) = 0 . Put μ = v + λ . Let H ' denote the set of all sequences ƒ ...
... denote the real axis , the Lebesgue measure on R , and v a finite positive λ - singular measure on R , so that there exists a A - null set e , such that v ( R − e1 ) = 0 . Put μ = v + λ . Let H ' denote the set of all sequences ƒ ...
Contents
SPECTRAL OPERATORS | 1924 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
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 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 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