Linear Operators: Spectral operators |
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Page 2325
... formulas ( 16 ) and ( 14 ) . It also follows , from Lemma 3.5 , formula ( 16 ) , and formula ( 14 ) , that the zero En of M ( u ) in R ) has the asymptotic representation -m §n ~ 2πn + a + z2 + Σ 5 m n − " m = 1 and that the zero E ...
... formulas ( 16 ) and ( 14 ) . It also follows , from Lemma 3.5 , formula ( 16 ) , and formula ( 14 ) , that the zero En of M ( u ) in R ) has the asymptotic representation -m §n ~ 2πn + a + z2 + Σ 5 m n − " m = 1 and that the zero E ...
Page 2330
... formula ( 26 ) that Em is given asymptotically by the formula ( 28 ) ( Emf ) ( t ) ~ n 2πί 0 n - Ĉ Axs ( μ + 2πn ) e1a + Aks ( μ + 2πn ) e ̄1a + A ′′ , ( μ + 2πn ) } k , j = 1 A ( μμ + 2πn ) etu + A ' ( μ + 2πn ) e - 1 " + A " ( μ + 2πn ) ...
... formula ( 26 ) that Em is given asymptotically by the formula ( 28 ) ( Emf ) ( t ) ~ n 2πί 0 n - Ĉ Axs ( μ + 2πn ) e1a + Aks ( μ + 2πn ) e ̄1a + A ′′ , ( μ + 2πn ) } k , j = 1 A ( μμ + 2πn ) etu + A ' ( μ + 2πn ) e - 1 " + A " ( μ + 2πn ) ...
Page 2341
... formula ( 58 ) , that the family of all sums ΣΕ MEJ m " J ranging over all finite sets of integers , is uniformly ... formula ( 56 ) and from formula ( 52 ) giving the form of the kernel G1 that if we excise from the angle A1 of the μ ...
... formula ( 58 ) , that the family of all sums ΣΕ MEJ m " J ranging over all finite sets of integers , is uniformly ... formula ( 56 ) and from formula ( 52 ) giving the form of the kernel G1 that if we excise from the angle A1 of the μ ...
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