Linear Operators: Spectral operators |
From inside the book
Results 1-3 of 89
Page 2013
... given by ( 9 ) and the domain of A consists precisely of those p for which the limit in ( 9 ) exists . Our next concern will be with the question of the existence of a resolution of the identity for A. This leads us to formulate the ...
... given by ( 9 ) and the domain of A consists precisely of those p for which the limit in ( 9 ) exists . Our next concern will be with the question of the existence of a resolution of the identity for A. This leads us to formulate the ...
Page 2088
... given by equations 12.4 . Show that if A is a scalar type spectral operator whose spectrum lies in a left half plane then it is the infinitesimal generator of the strongly continuous semi - group T ( t ) , t≥ 0 , given by the equation ...
... given by equations 12.4 . Show that if A is a scalar type spectral operator whose spectrum lies in a left half plane then it is the infinitesimal generator of the strongly continuous semi - group T ( t ) , t≥ 0 , given by the equation ...
Page 2096
... given , based on a theorem which asserts that , under certain hypotheses , a continuous linear mapping U of a Banach algebra 2 with unit e into B ( X ) is the projection of a continuous homomorphism of A into B ( X ) for some B - space ...
... given , based on a theorem which asserts that , under certain hypotheses , a continuous linear mapping U of a Banach algebra 2 with unit e into B ( X ) is the projection of a continuous homomorphism of A into B ( X ) for some B - space ...
Contents
SPECTRAL OPERATORS | 1924 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
35 other sections not shown
Other editions - View all
Common terms and phrases
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