Linear Operators: Spectral operators |
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Page 2249
... Theorem 9 ( v ) that ( 1 / f ) ( A ) is bounded . This proves the first two assertions of the present theorem , and also the inclusion o ( ƒ ( T ) ) ≤ ƒ ( o ( T ) ) , which is part of the final assertion of the present theorem . Since ...
... Theorem 9 ( v ) that ( 1 / f ) ( A ) is bounded . This proves the first two assertions of the present theorem , and also the inclusion o ( ƒ ( T ) ) ≤ ƒ ( o ( T ) ) , which is part of the final assertion of the present theorem . Since ...
Page 2403
... Theorem 1 in an illustrative but somewhat artificial setting , essentially to multiplication operators whose spectral measures are absolutely continuous with respect to two - dimensional Lebesgue measure . A first application ( Theorem ...
... Theorem 1 in an illustrative but somewhat artificial setting , essentially to multiplication operators whose spectral measures are absolutely continuous with respect to two - dimensional Lebesgue measure . A first application ( Theorem ...
Page 2418
... theorem ( III.11.14 ) , the integral ( 75 ) D ↓↓ 142 ( 2 ′′ , 2 ) | -- | A2 ( z , z ′ ) | | z — z'│ \ f ( z ' ) | dx ' dy ' dx dy exists for almost all z " € D. It follows from ( 65 ) and ( 68 ) , and from Fubini's theorem ( III.11.9 ) ...
... theorem ( III.11.14 ) , the integral ( 75 ) D ↓↓ 142 ( 2 ′′ , 2 ) | -- | A2 ( z , z ′ ) | | z — z'│ \ f ( z ' ) | dx ' dy ' dx dy exists for almost all z " € D. It follows from ( 65 ) and ( 68 ) , and from Fubini's theorem ( III.11.9 ) ...
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