Linear Operators, Part 2 |
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Page 2381
... solution of ( 7 — μ2 ) σ = 0 , ( t , μ ) e [ 0 , ∞ ) × Pt , 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 , ∞ ) × Pt , 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 Tou2o , 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 Tou2o , 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 - it 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 - it 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 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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 Borel function 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 eigenvalues elements equation exists finite number follows from Lemma 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