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 1986
Hence , to complete the proof of the theorem it suffices to establish the inversion
formula ( 5 ) . ... ( u ) du } dt = lim c { 1 , - oglu ) duzat = lim - 1 po a 07T1 - 00 sin
als – u ) $ - U - - P ( u ) du 1 poo sin at and so equation ( 5 ) may be established
by.
Hence , to complete the proof of the theorem it suffices to establish the inversion
formula ( 5 ) . ... ( u ) du } dt = lim c { 1 , - oglu ) duzat = lim - 1 po a 07T1 - 00 sin
als – u ) $ - U - - P ( u ) du 1 poo sin at and so equation ( 5 ) may be established
by.
Page 2212
We next establish the equation ( viii ) fpz = f Xo ( F ) , Fe B . To prove this , let g =
fz Xocp ) so that , using ( vii ) , we have g ( a ) = 0 for 1€ 07 . 0 ( F ) = 077 Also T ...
Thus if fz ( a ) = fw ( a ) on 0 , = 0w , equation ( ix ) will be established . Hence we
...
We next establish the equation ( viii ) fpz = f Xo ( F ) , Fe B . To prove this , let g =
fz Xocp ) so that , using ( vii ) , we have g ( a ) = 0 for 1€ 07 . 0 ( F ) = 077 Also T ...
Thus if fz ( a ) = fw ( a ) on 0 , = 0w , equation ( ix ) will be established . Hence we
...
Page 2234
Let x be in E ( e ) X and let x be in D ( f ( T | E ( e ) x ) ) . Then by Definition 8 ,
since ( ii ) has already been established for bounded Borel sets with closures
contained in U , f ( T | E ( e ) X ) x = lim f ( T | F ( en ) E ( e ) x ) F ( en ) x no = lim f (
T | E ...
Let x be in E ( e ) X and let x be in D ( f ( T | E ( e ) x ) ) . Then by Definition 8 ,
since ( ii ) has already been established for bounded Borel sets with closures
contained in U , f ( T | E ( e ) X ) x = lim f ( T | F ( en ) E ( e ) x ) F ( en ) x no = lim f (
T | E ...
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Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1929 |
Copyright | |
28 other sections not shown
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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 |