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 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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Common terms and phrases
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