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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Results 1-3 of 78
Page 1976
JEB SES Then for every bounded Borel scalar function y defined on the spectrum
o ( A ) , the integral ( ii ) o ( a ) E ( d ) ; Â ( s ) ) O ( A ) is an e - essentially bounded
E - measurable function of s . The integral ( iii ) Elo ; Â ( s ) ) e ( ds ) , 0EB , is a ...
JEB SES Then for every bounded Borel scalar function y defined on the spectrum
o ( A ) , the integral ( ii ) o ( a ) E ( d ) ; Â ( s ) ) O ( A ) is an e - essentially bounded
E - measurable function of s . The integral ( iii ) Elo ; Â ( s ) ) e ( ds ) , 0EB , is a ...
Page 1990
Here , we shall first be concerned with certain special examples of convolutions
which map H into H , which belong to the algebra A , and which have an integral
representation in one of the two forms ( 18 ) ( f * Q ) ( p ( s – t ) f ( t ) dt , QEH , RN
...
Here , we shall first be concerned with certain special examples of convolutions
which map H into H , which belong to the algebra A , and which have an integral
representation in one of the two forms ( 18 ) ( f * Q ) ( p ( s – t ) f ( t ) dt , QEH , RN
...
Page 2405
If he L ; ( S , E , p ) and 2 sr < 00 , it follows that the integral ( Ah ) ( 8 ) = S 14 ( 8 , t
) | h ( ) u ( dt ) ( 14 ) exists for u - almost all s , and that , writing fl . for the norm of
an element f of L ( S , E , u ) , we have Ahl , $ { A } , \ h \ , . Thus , using Theorem ...
If he L ; ( S , E , p ) and 2 sr < 00 , it follows that the integral ( Ah ) ( 8 ) = S 14 ( 8 , t
) | h ( ) u ( dt ) ( 14 ) exists for u - almost all s , and that , writing fl . for the norm of
an element f of L ( S , E , u ) , we have Ahl , $ { A } , \ h \ , . Thus , using Theorem ...
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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 |