Linear Operators: Spectral operators |
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Page 1931
... domain D ( f ) of an extension may contain points which cannot be connected with any point in p ( T ) by a curve in D ( f ) . 6 DEFINITION . The function R ( ; T ) x is said to have the single valued extension property provided that for ...
... domain D ( f ) of an extension may contain points which cannot be connected with any point in p ( T ) by a curve in D ( f ) . 6 DEFINITION . The function R ( ; T ) x is said to have the single valued extension property provided that for ...
Page 2087
... domain ( p ) T ( 24 ) ( RN ) is the infinitesimal generator of a strongly continuous semi - group S ( t ) , t≥ 0 ... domain D ( D ) of the natural closed extension of D contains ( p ) T ( 24 ) ( RN ) and the operator Ag + D + B with ...
... domain ( p ) T ( 24 ) ( RN ) is the infinitesimal generator of a strongly continuous semi - group S ( t ) , t≥ 0 ... domain D ( D ) of the natural closed extension of D contains ( p ) T ( 24 ) ( RN ) and the operator Ag + D + B with ...
Page 2256
... domain D1 containing the union of o ( T ) and a neighborhood of infinity , C1 being oriented in the customary positive sense of complex variable theory . The curves C of the present lemma bound a finite domain D containing every point ...
... domain D1 containing the union of o ( T ) and a neighborhood of infinity , C1 being oriented in the customary positive sense of complex variable theory . The curves C of the present lemma bound a finite domain D containing every point ...
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