Linear Operators: Spectral operators |
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Page 1976
... integral ( ii ) Soca , & ( A ) E ( dλ ; Â ( s ) ) is an e - essentially bounded E - measurable function of s . The integral ( iii ) √_ E ( σ ; Â ( 8 ) ) e ( ds ) , σε β , S is a bounded , countably additive spectral measure in Ho and ...
... integral ( ii ) Soca , & ( A ) E ( dλ ; Â ( s ) ) is an e - essentially bounded E - measurable function of s . The integral ( iii ) √_ E ( σ ; Â ( 8 ) ) e ( ds ) , σε β , S is a bounded , countably additive spectral measure in Ho and ...
Page 1990
... integral , that is , whether the integral is an ordinary Lebesgue integral defined for almost all s , a Cauchy type principal value integral defined as a certain limit of Lebesgue integrals , an integral of a vector valued function , or ...
... integral , that is , whether the integral is an ordinary Lebesgue integral defined for almost all s , a Cauchy type principal value integral defined as a certain limit of Lebesgue integrals , an integral of a vector valued function , or ...
Page 1991
... integral ( 21 ) X ( s ) = √e - istλ ( dt ) , SЄ RN , RN which will be used presently . The translation pt , however , is not compact valued , and we proceed as follows . For an H valued function ƒ , bounded and continuous on RN , and a ...
... integral ( 21 ) X ( s ) = √e - istλ ( dt ) , SЄ RN , RN which will be used presently . The translation pt , however , is not compact valued , and we proceed as follows . For an H valued function ƒ , bounded and continuous on RN , and a ...
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