Linear Operators: Spectral operators |
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Page 2307
... formal differential operators and sets of boundary conditions lead to spectral operators . As our treatment of this example makes clear , it suffices to study differential operators of the simple form ( d / dt ) and then to use Theorem ...
... formal differential operators and sets of boundary conditions lead to spectral operators . As our treatment of this example makes clear , it suffices to study differential operators of the simple form ( d / dt ) and then to use Theorem ...
Page 2318
... function and T be the unbounded differential operator defined by a formal differential operator T = - d \ 2 dx + q ( x ) and by the boundary conditions [ * ] . Then T is a spectral operator . PROOF . This follows immediately from ...
... function and T be the unbounded differential operator defined by a formal differential operator T = - d \ 2 dx + q ( x ) and by the boundary conditions [ * ] . Then T is a spectral operator . PROOF . This follows immediately from ...
Page 2371
... differential equations , and by C. E. Wilder [ 1 , 2 ] , who studied the case in which linear conditions are imposed at interior points of the interval of definition of a formal differential operator . The abstract operator - theoretic ...
... differential equations , and by C. E. Wilder [ 1 , 2 ] , who studied the case in which linear conditions are imposed at interior points of the interval of definition of a formal differential operator . The abstract operator - theoretic ...
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