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 TB , 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 TB , 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 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
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A₁ algebra Amer analytic applications arbitrary B-space Banach Banach space Boolean algebra Borel sets boundary bounded Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding defined Definition denote dense determined differential operator Doklady Akad elements equation equivalent established example exists extension finite follows formula function given gives H₁ Hence Hilbert space hypothesis identity integral invariant inverse Lemma limit linear operators Math multiplicity Nauk SSSR norm normal perturbation plane positive preceding present problem Proc projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero