Linear Operators: Spectral operators |
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Page 1985
... Fourier transform Fq of a function p in Ø is given by the integral 1 ( 4 ) ( Fq ) ( s ) = = ( 2π ) N / 2 √ , e - isto ( t ) dt , SЄ RN . RN The basic inversion formula for this integral is due to Fourier and is contained in the ...
... Fourier transform Fq of a function p in Ø is given by the integral 1 ( 4 ) ( Fq ) ( s ) = = ( 2π ) N / 2 √ , e - isto ( t ) dt , SЄ RN . RN The basic inversion formula for this integral is due to Fourier and is contained in the ...
Page 2174
... Fourier - Stieltjes transform of its resolution E of the identity ; hence E can be considered to be the inverse . Fourier - Stieltjes transform of the group { e - 2t | te R } . Assuming that this group is bounded in B ( x ) where X is ...
... Fourier - Stieltjes transform of its resolution E of the identity ; hence E can be considered to be the inverse . Fourier - Stieltjes transform of the group { e - 2t | te R } . Assuming that this group is bounded in B ( x ) where X is ...
Page 2175
... Fourier - Stieltjes transform exists . The following result was proved by Kantorovitz [ 4 ] : THEOREM . Let X be reflexive and let Te B ( X ) . Then the following statements are equivalent : ( 1 ) T is a scalar type spectral operator ...
... Fourier - Stieltjes transform exists . The following result was proved by Kantorovitz [ 4 ] : THEOREM . Let X be reflexive and let Te B ( X ) . Then the following statements are equivalent : ( 1 ) T is a scalar type spectral operator ...
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