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. 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. COROLLARY . Let q be a bounded measurable function and T be the unbounded differential operator defined by a formal differential ...
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