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 1976
The integral ( iii ) SE ( 0 ) E ( o ; Â ( 8 ) ) e ( ds ) , σε 8 , is a bounded , countably additive spectral measure in HP and ( iv ) So [ low , playE [ dA ; Â ( 0 ) ] elds ) = Sec , ecu [ [ [ da ; Ålo ) e ( do ) ] Ç ( A ) ( Sow ( a ) Â ...
The integral ( iii ) SE ( 0 ) E ( o ; Â ( 8 ) ) e ( ds ) , σε 8 , is a bounded , countably additive spectral measure in HP and ( iv ) So [ low , playE [ dA ; Â ( 0 ) ] elds ) = Sec , ecu [ [ [ da ; Ålo ) e ( do ) ] Ç ( A ) ( Sow ( a ) Â ...
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 ) ( S * q ) ( 3 ) = S ...
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 ) ( S * q ) ( 3 ) = S ...
Page 1991
This observation enables us to define the integral ( 21 ) f ( s ) = Se - ts ' ) ( dt ) , = - ) , 8 € RN RN which will be used presently . The translation qe , however , is not compact valued , and we proceed as follows .
This observation enables us to define the integral ( 21 ) f ( s ) = Se - ts ' ) ( dt ) , = - ) , 8 € RN RN which will be used presently . The translation qe , however , is not compact valued , and we proceed as follows .
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Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1929 |
Copyright | |
47 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 defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension 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 |