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 ) = [ 0 , ∞ ) × Pt , which coincides with ga ( 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 ) = [ 0 , ∞ ) × Pt , which coincides with ga ( 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 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 ...
Page 2394
... solution oз ( t , μ ) of the equation rσ = p2o , defined for 0 ≤t < ∞ and for all sufficiently small μ € P + , such that σ and σ's are continuous in t and μ for 0 ≤t < ∞ and μ sufficiently small , and such that as t σз ( t , μ ) ~ e ...
... solution oз ( t , μ ) of the equation rσ = p2o , defined for 0 ≤t < ∞ and for all sufficiently small μ € P + , such that σ and σ's are continuous in t and μ for 0 ≤t < ∞ and μ sufficiently small , and such that as t σз ( t , μ ) ~ e ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra 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 denote dense differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial PROOF properties prove quasi-nilpotent resolution Russian S₁ satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset subspace Suppose trace class type spectral operator unbounded uniformly bounded unique vector zero