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 t → ∞ . 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 t → ∞ . 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 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer arbitrary B*-algebra B₁ Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator Colojoară commuting compact complex numbers complex plane contains converges Corollary countably additive Definition dense differential operator disjoint Doklady Akad E-measurable eigenvalues elements equation equivalent exists Foias follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math matrix multiplicity norm operators in Hilbert perturbation polynomial PROOF proved quasi-nilpotent resolution restriction Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset subspace sufficiently type spectral operator unbounded unique vector weakly complete zero