Linear Operators: Spectral operators |
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Page 1991
... continuous and has its values in a compact set , it is A - measurable and thus integrable . For , in this case , the range of ƒ may be covered with a finite number of open sets G1 , ... , G2 , each having diameter less than a given ...
... continuous and has its values in a compact set , it is A - measurable and thus integrable . For , in this case , the range of ƒ may be covered with a finite number of open sets G1 , ... , G2 , each having diameter less than a given ...
Page 2066
... continuous map of RN into L1 ( XI.3.1 ( f ) ) and since h is continuous ( IX.2.3 ) , the inequality ( 7 ) shows that c ( t ) is continuous in t . Since fs * ft = fs + t * f we have h ( f ̧ ) h ( ft ) = h ( fs + t ) h ( f ) , which shows ...
... continuous map of RN into L1 ( XI.3.1 ( f ) ) and since h is continuous ( IX.2.3 ) , the inequality ( 7 ) shows that c ( t ) is continuous in t . Since fs * ft = fs + t * f we have h ( f ̧ ) h ( ft ) = h ( fs + t ) h ( f ) , which shows ...
Page 2448
... continuous spectrum . In the present section we shall illustrate this assertion by proving a number of results , due ... continuous linear mapping p : A → B ( X ) , of norm at most M1 , is given ; ( b ) a continuous linear mapping ŋ : A ...
... continuous spectrum . In the present section we shall illustrate this assertion by proving a number of results , due ... continuous linear mapping p : A → B ( X ) , of norm at most M1 , is given ; ( b ) a continuous linear mapping ŋ : A ...
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