Linear Operators: Spectral operators |
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Page 1976
... integral ( ii ) Ф Sa P ( X ) E ( dλ ; Â ( 8 ) ) σ ( A ) is an e - essentially bounded E - measurable function of s . The integral ( iii ) [ _E ( σ ; Â ( 8 ) ) e ( ds ) , σε , is a bounded , countably additive spectral measure in HP and ...
... integral ( ii ) Ф Sa P ( X ) E ( dλ ; Â ( 8 ) ) σ ( A ) is an e - essentially bounded E - measurable function of s . The integral ( iii ) [ _E ( σ ; Â ( 8 ) ) e ( ds ) , σε , is a bounded , countably additive spectral measure in HP 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 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer arbitrary B*-algebra B₁ Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator Colojoară commuting compact complex numbers complex plane contains converges Corollary countably additive Definition dense differential operator disjoint Doklady Akad E-measurable eigenvalues elements equation equivalent exists Foias follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math matrix multiplicity norm operators in Hilbert perturbation polynomial PROOF proved quasi-nilpotent resolution restriction Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset subspace sufficiently type spectral operator unbounded unique vector weakly complete zero