Linear Operators: Spectral operators |
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Page 2384
... solution " of the differential equation Tσ = μ2o , that is , the solution asymptotic to e iut 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 iut 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 - it as too . 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 - it as too . 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 o ( t , μ ) of the equation Tσ = p2o , defined for 0 ≤t < ∞ and for all sufficiently small μ € P + , such that σ , and og are continuous in t and μ for 0 ≤t < ∞ and μ sufficiently small , and such that σз ( t , μ ) ~ e ...
... solution o ( t , μ ) of the equation Tσ = p2o , defined for 0 ≤t < ∞ and for all sufficiently small μ € P + , such that σ , and og are continuous in t and μ for 0 ≤t < ∞ and μ sufficiently small , and such that σз ( t , μ ) ~ e ...
Contents
SPECTRAL OPERATORS | 1924 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
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A₁ algebra Amer analytic applications arbitrary B-space Banach Banach space Boolean algebra Borel sets boundary bounded Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding defined Definition denote dense determined differential operator Doklady Akad elements equation equivalent established example exists extension finite follows formula function given gives H₁ Hence Hilbert space hypothesis identity integral invariant inverse Lemma limit linear operators Math multiplicity Nauk SSSR norm normal perturbation plane positive preceding present problem Proc projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero