Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |
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Page 2330
... formula ( 21 ) , we have only to take the residues at Em and έm of the contour integral ( 27 ) С ( nμ ” - 1R ( μ TM ... formula ( 26 ) that Em is given asymptotically by the formula ( 28 ) ( Emf ) ( t ) ~ n 2πί Sco Co Ľ 1 n Ĉ Аxs ( μ + ...
... formula ( 21 ) , we have only to take the residues at Em and έm of the contour integral ( 27 ) С ( nμ ” - 1R ( μ TM ... formula ( 26 ) that Em is given asymptotically by the formula ( 28 ) ( Emf ) ( t ) ~ n 2πί Sco Co Ľ 1 n Ĉ Аxs ( μ + ...
Page 2340
... formula ( 42 ) . It now follows just as in Case 1A that the projection Em = E ( m ; T ) is given asymptotically by the formula n 1 ( 57 ) ( Emf ) ( x ) n { Ê ̧ Axs ( μ + 2mm ) e1u + Aks ( μ + 2πm ) Σ ( k , j = 1 ἐμ 0 A ( μ + 2πm ) е11 + ...
... formula ( 42 ) . It now follows just as in Case 1A that the projection Em = E ( m ; T ) is given asymptotically by the formula n 1 ( 57 ) ( Emf ) ( x ) n { Ê ̧ Axs ( μ + 2mm ) e1u + Aks ( μ + 2πm ) Σ ( k , j = 1 ἐμ 0 A ( μ + 2πm ) е11 + ...
Page 2341
... formula ( 58 ) , that the family of all sums ΣΕ , Em MEJ J ranging over all finite sets of integers , is uniformly ... formula ( 56 ) and from formula ( 52 ) giving the form of the kernel G , that if we excise from the angle A1 of the μ ...
... formula ( 58 ) , that the family of all sums ΣΕ , Em MEJ J ranging over all finite sets of integers , is uniformly ... formula ( 56 ) and from formula ( 52 ) giving the form of the kernel G , that if we excise from the angle A1 of the μ ...
Contents
SPECTRAL OPERATORS | 1924 |
The Spectrum of a Spectral Operator | 1955 |
The Algebras A and | 1966 |
Copyright | |
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A₁ Acad adjoint operator algebra of projections Amer analytic arbitrary B-algebra B-space B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition dense differential operator Dokl Doklady Akad eigenvalues elements equation exists formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis ibid identity inequality invariant subspaces inverse Krein L₁ Lemma locally convex spaces multiplicity Nauk SSSR nonselfadjoint norm normal operators operators in Hilbert perturbation Proc PROOF properties prove Pures Appl quasi-nilpotent resolution Russian satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose topology trace class type spectral operator unbounded uniformly bounded vector zero