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 89
Page 2299
Hence we find that for n sufficiently large , each u in Cn is in plT + P ) and that R (
j ; T + P ) = B ( u ) . Since Blu ) is clearly the product of the compact operator R ( u
; T ) and a bounded operator , it follows that T + P is a discrete operator .
Hence we find that for n sufficiently large , each u in Cn is in plT + P ) and that R (
j ; T + P ) = B ( u ) . Since Blu ) is clearly the product of the compact operator R ( u
; T ) and a bounded operator , it follows that T + P is a discrete operator .
Page 2360
It will be shown below that | T ' ' R ( u ; T ) A S | for u in V , and i sufficiently large .
From this it will then follow as above that the function f ( u ) = R ( u ; T + P ) f is
uniformly bounded . It will also be shown that T - v is compact . From this , ( iii ) ,
and ...
It will be shown below that | T ' ' R ( u ; T ) A S | for u in V , and i sufficiently large .
From this it will then follow as above that the function f ( u ) = R ( u ; T + P ) f is
uniformly bounded . It will also be shown that T - v is compact . From this , ( iii ) ,
and ...
Page 2394
Let the hypotheses of Corollary 2 be satisfied . Then there exists a solution oz ( t ,
u ) of the equation to = u o , defined for 0 St < oo and for all sufficiently small u e P
+ , such that oz and os are continuous in t and Me for 0 St < 0 and u sufficiently ...
Let the hypotheses of Corollary 2 be satisfied . Then there exists a solution oz ( t ,
u ) of the equation to = u o , defined for 0 St < oo and for all sufficiently small u e P
+ , such that oz and os are continuous in t and Me for 0 St < 0 and u sufficiently ...
What people are saying - Write a review
We haven't found any reviews in the usual places.
Contents
SPECTRAL OPERATORS XV Spectral Operators | 1924 |
Introduction | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
32 other sections not shown
Other editions - View all
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 |