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 ( A , ) for all n and ΣA , Ex ... denote the range of the resolution of the identity E ( · ) of Q 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 ( A , ) for all n and ΣA , Ex ... denote the range of the resolution of the identity E ( · ) of Q 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 algebra Amer analytic applications arbitrary B-space Banach Banach space Boolean algebra Borel sets boundary bounded Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding defined Definition denote dense determined differential operator Doklady Akad elements equation equivalent established example exists extension finite follows formula function given gives H₁ Hence Hilbert space hypothesis identity integral invariant inverse Lemma limit linear operators Math multiplicity Nauk SSSR norm normal perturbation plane positive preceding present problem Proc projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero