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
By considering the integral as an iterated integral , it is seen that it suffices to
establish ( 5 ) in the case N = 1 . In this case the right side ... plu ) du S - U sin at =
lim - PIS – t ) - dt , _ and so equation ( 5 ) may be established by. 0 - 700 1986 XV
.
By considering the integral as an iterated integral , it is seen that it suffices to
establish ( 5 ) in the case N = 1 . In this case the right side ... plu ) du S - U sin at =
lim - PIS – t ) - dt , _ and so equation ( 5 ) may be established by. 0 - 700 1986 XV
.
Page 2101
Such a formula has been established by Foguel [ 1 ] under the hypotheses that ( i
) the Boolean algebra generated by E , and E , is bounded , ( ii ) X is weakly
complete , and ( iii ) the E - measure of the boundary of o is zero . Further work
along ...
Such a formula has been established by Foguel [ 1 ] under the hypotheses that ( i
) the Boolean algebra generated by E , and E , is bounded , ( ii ) X is weakly
complete , and ( iii ) the E - measure of the boundary of o is zero . Further work
along ...
Page 2212
We next establish the equation ( viii ) fro = f : Xocp ) , Fe B . To prove this , let g =
fz Xocp ) so that , using ( vii ) , we have g ( 1 ) = 0 for 1€ 0 , 0 ( F ) = 0ft . Also T ( g )
... Thus if fz ( a ) = fw ( a ) on 0 , = ow , equation ( ix ) will be established . Hence ...
We next establish the equation ( viii ) fro = f : Xocp ) , Fe B . To prove this , let g =
fz Xocp ) so that , using ( vii ) , we have g ( 1 ) = 0 for 1€ 0 , 0 ( F ) = 0ft . Also T ( g )
... Thus if fz ( a ) = fw ( a ) on 0 , = ow , equation ( ix ) will be established . Hence ...
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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 |