Linear Operators: Spectral operators |
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Page 1916
... obtained in the first sections of Chapter XIX , but which can be proved under hypotheses which are considerably more general ; their proofs rest ultimately on the generalized Carleman inequalities of Chapter X. Chapter XX is devoted to ...
... obtained in the first sections of Chapter XIX , but which can be proved under hypotheses which are considerably more general ; their proofs rest ultimately on the generalized Carleman inequalities of Chapter X. Chapter XX is devoted to ...
Page 2103
... obtained by replacing 1 / A by any function ƒ ( A ) analytic for λ in a neighborhood of the spectrum of the element a in A1 are extensions of the results to be found in IX.4.10 and IX.4.11 . The elementary Lemma 6 which permits these ...
... obtained by replacing 1 / A by any function ƒ ( A ) analytic for λ in a neighborhood of the spectrum of the element a in A1 are extensions of the results to be found in IX.4.10 and IX.4.11 . The elementary Lemma 6 which permits these ...
Page 2176
... obtained . Similar results were also obtained by Dollinger [ 1 ] and Sine [ 1 ] under the hypothesis that T satisfies certain types of operational calculi , although their assumptions were quite different in nature . Stampfli [ 12 ] has ...
... obtained . Similar results were also obtained by Dollinger [ 1 ] and Sine [ 1 ] under the hypothesis that T satisfies certain types of operational calculi , although their assumptions were quite different in nature . Stampfli [ 12 ] has ...
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