Linear Operators: Spectral operators |
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Page 1930
... plane which contains the void set and the whole plane , in short , if Σ is a field of sets in the complex plane , then a spectral measure E on Σ is called a resolution of the identity ( or a spectral resolution ) for the operator T if E ...
... plane which contains the void set and the whole plane , in short , if Σ is a field of sets in the complex plane , then a spectral measure E on Σ is called a resolution of the identity ( or a spectral resolution ) for the operator T if E ...
Page 2087
... plane R ( S ) > 0 . For every ( 0 ) in Ho there is one and only one continuous map t → q ( t ) of [ 0 , ∞ ) into HP which is differentiable for t > 0 and has the properties p ( t ) e ( p ) T ( 24 ) ( RN ) , ( ii ) 0 < t < ∞ , ( iii ) ...
... plane R ( S ) > 0 . For every ( 0 ) in Ho there is one and only one continuous map t → q ( t ) of [ 0 , ∞ ) into HP which is differentiable for t > 0 and has the properties p ( t ) e ( p ) T ( 24 ) ( RN ) , ( ii ) 0 < t < ∞ , ( iii ) ...
Page 2335
... plane , let μ ( λ ) denote that unique nth root of λ which lies in the angular sector { μ | π / 2n ≥ ( arg μ ) -T / 2n } of the complex plane . Put ( 34 ) σx ( t , μ ) = e ρίμωκτ 0 ≤ k ≤v , = еiuwk ( t − 1 ) , - v ≤ k ≤ 2v . = e ...
... plane , let μ ( λ ) denote that unique nth root of λ which lies in the angular sector { μ | π / 2n ≥ ( arg μ ) -T / 2n } of the complex plane . Put ( 34 ) σx ( t , μ ) = e ρίμωκτ 0 ≤ k ≤v , = еiuwk ( t − 1 ) , - v ≤ k ≤ 2v . = e ...
Contents
SPECTRAL OPERATORS | 1924 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
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A₁ adjoint operator 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 operators 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 sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero