Linear Operators: Spectral operators |
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Page 1962
... corresponding upper and lower case letters for corresponding elements . It is clear that the mapping A↔ ( a1 , ) is linear . It is , in fact , an algebraic isomorphism between the algebras B ( S ) and M , ( B ( H ) ) , for if A↔ ( a ...
... corresponding upper and lower case letters for corresponding elements . It is clear that the mapping A↔ ( a1 , ) is linear . It is , in fact , an algebraic isomorphism between the algebras B ( S ) and M , ( B ( H ) ) , for if A↔ ( a ...
Page 2305
... corresponding to these eigen- values is one - dimensional . It follows immediately from Corollary 9 that L + B is a ... corresponding eigenfunctions ( the corresponding projections having one- dimensional ranges ) are e2nin , n = 0 , ± 1 ...
... corresponding to these eigen- values is one - dimensional . It follows immediately from Corollary 9 that L + B is a ... corresponding eigenfunctions ( the corresponding projections having one- dimensional ranges ) are e2nin , n = 0 , ± 1 ...
Page 2507
... corresponding to a two- body force in a three - body system ) , then the spectrum of H + V consists of the purely continuous spectrum corresponding to the spectrum of H , a point spectrum corresponding to the " bound states " of the ...
... corresponding to a two- body force in a three - body system ) , then the spectrum of H + V consists of the purely continuous spectrum corresponding to the spectrum of H , a point spectrum corresponding to the " bound states " of the ...
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