Linear Operators: Spectral operators |
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Page 1990
... vector valued function , or a principal value integral of a vector valued function . For a given in H and a point t in RN the translate q , in H , defined as Pt Pt ( s ) = q ( st ) , when regarded as a map t → o , of RN into 5 , is ...
... vector valued function , or a principal value integral of a vector valued function . For a given in H and a point t in RN the translate q , in H , defined as Pt Pt ( s ) = q ( st ) , when regarded as a map t → o , of RN into 5 , is ...
Page 2160
... vector x in X is the sum of a vector y with ( λ 。 I — T ) y = 0 and a vector x - - y in the closure of ( I − T ) X . Since λo is interior to an interval of constancy relative to T , it is therefore a regular point relative to ...
... vector x in X is the sum of a vector y with ( λ 。 I — T ) y = 0 and a vector x - - y in the closure of ( I − T ) X . Since λo is interior to an interval of constancy relative to T , it is therefore a regular point relative to ...
Page 2266
... vector x is sp { Ex | E e B ) . A projection E e B will be said to satisfy the countable chain condition if every family of disjoint projections in B bounded by E is at most countable . We shall denote by the set of all E e B satisfying ...
... vector x is sp { Ex | E e B ) . A projection E e B will be said to satisfy the countable chain condition if every family of disjoint projections in B bounded by E is at most countable . We shall denote by the set of all E e B satisfying ...
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