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 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
... operator ( d / dt ) 2 and with arbitrary separated boundary conditions , are spectral operators . We begin with a general lemma relating the spectrum and the point spectrum of a differential operator . The reader to whom the notation ...
... operator ( d / dt ) 2 and with arbitrary separated boundary conditions , are spectral operators . We begin with a general lemma relating the spectrum and the point spectrum of a differential operator . The reader to whom the notation ...
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 |
The Resolvent of a Spectral Operator | 1935 |
An Operational Calculus for Bounded Spectral | 1941 |
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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