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 $ ; T ) .x will be meant an X - valued function f defined and analytic on an open set D ( S ) 2p ( T ) and such that ( $ I - T ' ) f ( $ ) = x , & € D ( S ) .
If x is a vector in X , then by an analytic extension of R $ ; T ) .x will be meant an X - valued function f defined and analytic on an open set D ( S ) 2p ( T ) and such that ( $ I - T ' ) f ( $ ) = x , & € D ( S ) .
Page 1932
In this case x ( $ ) is a single valued analytic function with domain pla ) and with x ( K ) = R ( £ ; T ) x , ξερ ( T ' ) . It will be shown in the next section that , if T is a spectral operator , the function R ( $ ; T ' ) x has ...
In this case x ( $ ) is a single valued analytic function with domain pla ) and with x ( K ) = R ( £ ; T ) x , ξερ ( T ' ) . It will be shown in the next section that , if T is a spectral operator , the function R ( $ ; T ' ) x has ...
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 ...
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 ...
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Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1929 |
Copyright | |
47 other sections not shown
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Common terms and phrases
adjoint operator Amer analytic apply arbitrary assumed B-space Banach space belongs Boolean algebra Borel set boundary conditions bounded bounded operator Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear operator Math Moreover multiplicity norm perturbation plane positive preceding present problem projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type seen sequence shown shows similar solution spectral measure spectral operator spectrum subset sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector 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 |