Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |
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Page 1931
If x is a vector in X , then by an analytic extension of R ( É ; T ) x will be meant an
X - valued function f defined and analytic on an open set D ( ) 2 p ( T ) and such
that ( ŠI — T ) f ( 6 ) = x , ŠE D ( f ) . It is clear that , for such an extension , f ( $ ) =
R ...
If x is a vector in X , then by an analytic extension of R ( É ; T ) x will be meant an
X - valued function f defined and analytic on an open set D ( ) 2 p ( T ) and such
that ( ŠI — T ) f ( 6 ) = x , ŠE D ( f ) . It is clear that , for such an extension , f ( $ ) =
R ...
Page 1932
In this case x ( 5 ) is a single valued analytic function with domain p ( x ) and with
X ( $ ) = R ( É ; T ) x , Šep ( T ) . It will be shown in the next section that , if T is a
spectral operator , the function R ( £ ; T ' ) x has , for every x in X , the single
valued ...
In this case x ( 5 ) is a single valued analytic function with domain p ( x ) and with
X ( $ ) = R ( É ; T ) x , Šep ( T ) . It will be shown in the next section that , if T is a
spectral operator , the function R ( £ ; T ' ) x has , for every x in X , the single
valued ...
Page 2248
Let f be a function analytic in a domain U which , when taken together with a finite
number of exceptional points p , includes a neighborhood of o ( T ) and a
neighborhood of the point at infinity . Suppose that each exceptional point p
satisfies E ...
Let f be a function analytic in a domain U which , when taken together with a finite
number of exceptional points p , includes a neighborhood of o ( T ) and a
neighborhood of the point at infinity . Suppose that each exceptional point p
satisfies E ...
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Contents
SPECTRAL OPERATORS XV Spectral Operators | 1924 |
Introduction | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
32 other sections not shown
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Common terms and phrases
analytic apply arbitrary assumed B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded Borel bounded operator Chapter clear clearly closure commuting compact complex consider constant contained converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established example exists extension fact finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm positive preceding present problem projections PROOF properties prove range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows spectral measure spectral operator spectrum statement strongly subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero
Bibliographic information
| Title | Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 Pure and applied mathematics, v. 7 |
| Authors | Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle |
| Editors | L. Bers, J. J. Stoker |
| Publisher | Wiley-Interscience, 1957 |
| Original from | the University of Michigan |
| Digitized | 2 Feb 2010 |
| ISBN | 0471226394, 9780471226390 |
| Length | 667 pages |
| Export Citation | BiBTeX EndNote RefMan |