Linear Operators: Spectral operators |
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Page 2290
... differential operators . We let the unperturbed operator T be a simple nth order differential operator i - " ( d / dt ) " , restricted by a set of boundary conditions subject to certain broad conditions of regularity . It then follows ...
... differential operators . We let the unperturbed operator T be a simple nth order differential operator i - " ( d / dt ) " , restricted by a set of boundary conditions subject to certain broad conditions of regularity . It then follows ...
Page 2307
... differential operators and sets of boundary conditions lead to spectral operators . As our treatment of this example ... Operator In this section Corollary 2.9 will be applied to show that operators of the form T + B , where B is an arbitrary ...
... differential operators and sets of boundary conditions lead to spectral operators . As our treatment of this example ... Operator In this section Corollary 2.9 will be applied to show that operators of the form T + B , where B is an arbitrary ...
Page 2318
... operator , T + B is a spectral operator . PROOF . This follows from Lemma 10 and Corollary 2.9 . Q.E.D. 12 COROLLARY . Let q be a bounded measurable function and T be the unbounded differential operator defined by a formal differential ...
... operator , T + B is a spectral operator . PROOF . This follows from Lemma 10 and Corollary 2.9 . Q.E.D. 12 COROLLARY . Let q be a bounded measurable function and T be the unbounded differential operator defined by a formal differential ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary asymptotic B₁ Banach space Boolean algebra Borel set boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complete Boolean algebra complex numbers complex plane continuous functions converges Corollary countably additive Definition denote differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem follows immediately formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality inverse L₁ Lebesgue Math multiplicity Nauk SSSR norm operators in Hilbert perturbation PROOF properties prove quasi-nilpotent resolution Russian satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose trace class type spectral operator unbounded uniformly bounded vector zero