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 2384
... asymptotic to e - tut as too . Since , in contrast to σ1 , such a solution is not uniquely determined by its asymptotic form , we meet a number of additional , slight , technical complications in the asymptotic analysis of such ...
... asymptotic to e - tut as too . Since , in contrast to σ1 , such a solution is not uniquely determined by its asymptotic form , we meet a number of additional , slight , technical complications in the asymptotic analysis of such ...
Page 2394
... asymptotic to e itu as t → ∞ and whose derivative is asymptotic to iμettu as t → ∞ . Then ôз ( t , μ ) = a ( μ ) σ1 ( t , μ ) + b ( μ ) σ2 ( t , μ ) for suitable functions a ( μ ) and b ( μ ) . It is evident from the asymptotic form ...
... asymptotic to e itu as t → ∞ and whose derivative is asymptotic to iμettu as t → ∞ . Then ôз ( t , μ ) = a ( μ ) σ1 ( t , μ ) + b ( μ ) σ2 ( t , μ ) for suitable functions a ( μ ) and b ( μ ) . It is evident from the asymptotic form ...
Page 2399
... asymptotic relation- ships σ1 ( t ) ~ 1 , 02 ( t ) ~ t as t → ∞ . PROOF . We saw in Corollary 2 that o1 ( t ) = σ1 ( t , 0 ) satisfies the first of these asymptotic relationships . Let a be so large that o1 ( t ) 0 for a≤too . Then ...
... asymptotic relation- ships σ1 ( t ) ~ 1 , 02 ( t ) ~ t as t → ∞ . PROOF . We saw in Corollary 2 that o1 ( t ) = σ1 ( t , 0 ) satisfies the first of these asymptotic relationships . Let a be so large that o1 ( t ) 0 for a≤too . Then ...
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