Linear Operators: Spectral operators |
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Page 1931
... clear to begin with that a countably additive resolution of the identity defined on the Borel sets of the plane is uniquely determined by the spectral operator T. This is the case , but until it is proved we refer to any such spectral ...
... clear to begin with that a countably additive resolution of the identity defined on the Borel sets of the plane is uniquely determined by the spectral operator T. This is the case , but until it is proved we refer to any such spectral ...
Page 2053
... clear from the form of exp t that T ( t ) was differentiable for t > 0 and an arbitrary in 5 " . It is even clear that the nth order derivative T ) ( t ) exists in the uniform operator topology for t > 0 and every positive integer n ...
... clear from the form of exp t that T ( t ) was differentiable for t > 0 and an arbitrary in 5 " . It is even clear that the nth order derivative T ) ( t ) exists in the uniform operator topology for t > 0 and every positive integer n ...
Page 2159
... clear that the union of intervals of constancy is open . To see that it is dense , let y be a closed subarc of П , having positive length and let Yn = { λo | λo € y , | λ — λ 。| " | R ( λ ; T ) | ≤ 1 , do ‡ λ € 4x0 } = { λo | λo € y ...
... clear that the union of intervals of constancy is open . To see that it is dense , let y be a closed subarc of П , having positive length and let Yn = { λo | λo € y , | λ — λ 。| " | R ( λ ; T ) | ≤ 1 , do ‡ λ € 4x0 } = { λo | λo € y ...
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