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 2381
... solution of ( 7 — μ2 ) σ = 0 , ( t , μ ) e [ 0 , ∞ ) × P , which coincides with gu ( t ) for t≥a ( cf. Corollary ... solution of equation ( 7 ) which exists in C [ a ,, ∞ ) , by the above . Then , by the uniqueness of the solution of ...
... solution of ( 7 — μ2 ) σ = 0 , ( t , μ ) e [ 0 , ∞ ) × P , which coincides with gu ( t ) for t≥a ( cf. Corollary ... solution of equation ( 7 ) which exists in C [ a ,, ∞ ) , by the above . Then , by the uniqueness of the solution of ...
Page 2384
... solution " of the differential equation Tσ = μ2o , that is , the solution 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 ...
... solution " of the differential equation Tσ = μ2o , that is , the solution 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 ...
Page 2391
... solution " σ2 ( t , λ ) constructed in Lemma 3 by any solution asymptotic to e as t → ∞o . Appropriate choice of this second solution will enable us to calcu- late finer properties of the resolvent as needed below . The following ...
... solution " σ2 ( t , λ ) constructed in Lemma 3 by any solution asymptotic to e as t → ∞o . Appropriate choice of this second solution will enable us to calcu- late finer properties of the resolvent as needed below . The following ...
Contents
SPECTRAL OPERATORS | 1924 |
An Operational Calculus for Bounded Spectral | 1941 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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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 inverse Krein L₁ Lemma locally convex spaces multiplicity Nauk SSSR norm normal operators operators in Hilbert perturbation polynomial Proc PROOF properties prove Pure Appl quasi-nilpotent resolution Russian S₁ 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