Linear Operators: Spectral operators |
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Page 2307
... boundary conditions lead to spectral operators . As our treatment of this example makes clear , it suffices to study differential operators of the simple ... BOUNDARY CONDITIONS Separated Boundary Conditions for the Second Order Operator.
... boundary conditions lead to spectral operators . As our treatment of this example makes clear , it suffices to study differential operators of the simple ... BOUNDARY CONDITIONS Separated Boundary Conditions for the Second Order Operator.
Page 2344
... boundary conditions , of which n / 2 are boundary conditions at zero and n / 2 are boundary conditions at 1. Then all the conclusions of Theorem 8 are valid . In this connection , it is also worth making a simple remark on the notion of ...
... boundary conditions , of which n / 2 are boundary conditions at zero and n / 2 are boundary conditions at 1. Then all the conclusions of Theorem 8 are valid . In this connection , it is also worth making a simple remark on the notion of ...
Page 2350
... boundary conditions C1 ( Uƒ ) = 0 is regular ) to assume that an - 1 ( t ) = 0. But , under the condition that the set of boundary conditions C ( Uf ) = 0 is regular , this has been established above . Thus , to complete the proof , it ...
... boundary conditions C1 ( Uƒ ) = 0 is regular ) to assume that an - 1 ( t ) = 0. But , under the condition that the set of boundary conditions C ( Uf ) = 0 is regular , this has been established above . Thus , to complete the proof , it ...
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