Linear Operators: Spectral operators |
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Results 1-3 of 43
Page 1985
... 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 following ...
... 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 following ...
Page 2000
... transform p ( t ) dt , Pε H , ( hq ) ( 8 ) = 1.i.m. - > t 0 + 3 ( 34 ) is in 2 and has ( 35 ) h : - ---- πι sgn s e ( ds ) , | h | = π . 16 EXAMPLE ( Calderón and Zygmund ) . An analogue of the Hilbert transform in case the dimension N ...
... transform p ( t ) dt , Pε H , ( hq ) ( 8 ) = 1.i.m. - > t 0 + 3 ( 34 ) is in 2 and has ( 35 ) h : - ---- πι sgn s e ( ds ) , | h | = π . 16 EXAMPLE ( Calderón and Zygmund ) . An analogue of the Hilbert transform in case the dimension N ...
Page 2175
... 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 with real spectrum ...
... 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 with real spectrum ...
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