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 |
From inside the book
Results 1-3 of 79
Page 1933
The Resolvent of a Spectral Operator The vector valued analytic functions R ( E ;
T ' ) x associated with the resolvent of a bounded spectral operator have a
number of important properties not enjoyed by functions of the form RTÉ ; T ) x
when T ...
The Resolvent of a Spectral Operator The vector valued analytic functions R ( E ;
T ' ) x associated with the resolvent of a bounded spectral operator have a
number of important properties not enjoyed by functions of the form RTÉ ; T ) x
when T ...
Page 2291
Since the notion of an operator with compact resolvent occurs so frequently in
this section , it will be convenient to introduce , in the following definition , a
special term for such operators . + 1 DEFINITION . An operator T is discrete if
there is a ...
Since the notion of an operator with compact resolvent occurs so frequently in
this section , it will be convenient to introduce , in the following definition , a
special term for such operators . + 1 DEFINITION . An operator T is discrete if
there is a ...
Page 2316
... Adjoint Operators in Hilbert Space Nelson Dunford, Jacob Theodore Schwartz.
Thus , if E ( ) n ) is to be anything but a projection onto a one - dimensional range
, it follows from Lemma 2 . 2 that in must be a multiple pole of the resolvent .
... Adjoint Operators in Hilbert Space Nelson Dunford, Jacob Theodore Schwartz.
Thus , if E ( ) n ) is to be anything but a projection onto a one - dimensional range
, it follows from Lemma 2 . 2 that in must be a multiple pole of the resolvent .
What people are saying - Write a review
We haven't found any reviews in the usual places.
Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1929 |
Copyright | |
28 other sections not shown
Other editions - View all
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 countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension fact 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 |