Linear Operators: Spectral operators |
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Page 1976
... integral ( ii ) Sau , P ( X ) E ( dλ ; Â ( s ) ) is an e - essentially bounded E - measurable function of s . The integral ( iii ) | _ E ( o ; Â ( s ) ) e ( ds ) , σ € B , is a bounded , countably additive spectral measure in Ho and ...
... integral ( ii ) Sau , P ( X ) E ( dλ ; Â ( s ) ) is an e - essentially bounded E - measurable function of s . The integral ( iii ) | _ E ( o ; Â ( s ) ) e ( ds ) , σ € B , 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 ( 8 ) = √ . Sav RN e - istλ ( dt ) , SЄ RN , which will be used presently . The translation pt , however , is not compact valued , and we proceed as follows . For an H valued function f , bounded and continuous on RN ...
... integral ( 21 ) X ( 8 ) = √ . Sav RN e - istλ ( dt ) , SЄ RN , which will be used presently . The translation pt , however , is not compact valued , and we proceed as follows . For an H valued function f , bounded and continuous on RN ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary asymptotic B₁ Banach space Boolean algebra Borel set boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complete Boolean algebra complex numbers complex plane continuous functions converges Corollary countably additive Definition denote differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem follows immediately formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality inverse L₁ Lebesgue Math multiplicity Nauk SSSR norm operators in Hilbert perturbation PROOF properties prove quasi-nilpotent resolution Russian satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose trace class type spectral operator unbounded uniformly bounded vector zero