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 2425
If we put + oo ( 33 ) ( T ( B ) f ) ( s ) = 1 B ( s , 0 ) f ( o ) do , - - 00 8 - 0 it follows from Lemma 5 and from ( 31 ) and ( 32 ) that there exists a finite constant N ( y , B ) depending only on y and ß such that + 1/2 +00 1/2 ...
If we put + oo ( 33 ) ( T ( B ) f ) ( s ) = 1 B ( s , 0 ) f ( o ) do , - - 00 8 - 0 it follows from Lemma 5 and from ( 31 ) and ( 32 ) that there exists a finite constant N ( y , B ) depending only on y and ß such that + 1/2 +00 1/2 ...
Page 2439
Since there exists a positive constant co such that ( sin 0 2 colsin ( 0/2 ) for 0 5 10 $ / 2 , formula ( 30 ) follows at once . Using ( 27 ) , ( 30 ) , and ( 31 ) , we see that there exists a finite constant M ' independent of ε such ...
Since there exists a positive constant co such that ( sin 0 2 colsin ( 0/2 ) for 0 5 10 $ / 2 , formula ( 30 ) follows at once . Using ( 27 ) , ( 30 ) , and ( 31 ) , we see that there exists a finite constant M ' independent of ε such ...
Page 2441
This shows that there exists a finite absolute constant c ' such that I ( Q ) ] = c ' ( 1 + 1 & 1 ) -n + 1 . Using this inequality and using ( 37 ) , we see that there exists a finite constant M " independent of ε such that av av 22V ...
This shows that there exists a finite absolute constant c ' such that I ( Q ) ] = c ' ( 1 + 1 & 1 ) -n + 1 . Using this inequality and using ( 37 ) , we see that there exists a finite constant M " independent of ε such that av av 22V ...
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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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Common terms and phrases
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 |