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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3 that pl ( Â ( s ) ) = 0 almost everywhere on S . Thus , for almost all s , o vanishes
on the spectrum o ( Â ( s ) ) . So , for some set o , in { with eloo ) = e , the function
o vanishes on Uses , O ( Â ( s ) ) , and since y is continuous , it also vanishes on ...
3 that pl ( Â ( s ) ) = 0 almost everywhere on S . Thus , for almost all s , o vanishes
on the spectrum o ( Â ( s ) ) . So , for some set o , in { with eloo ) = e , the function
o vanishes on Uses , O ( Â ( s ) ) , and since y is continuous , it also vanishes on ...
Page 2343
Consequently , if we use Lagrange ' s rule to expand this 2v x 2v determinant by
minors of order v , we find that the expansion contains only two non - vanishing
terms . Thus our 2v X 2v determinant may be expressed as P2P , FQ1Q2 , where
...
Consequently , if we use Lagrange ' s rule to expand this 2v x 2v determinant by
minors of order v , we find that the expansion contains only two non - vanishing
terms . Thus our 2v X 2v determinant may be expressed as P2P , FQ1Q2 , where
...
Page 2468
Let q be a non - negative function belonging to C ( R ) , vanishing outside [ - 1 , +
1 ] , and satisfying Q ( x ) = 9 ( - x ) and Se ola ) da = 1 . For each E > 0 , and each
BEH ' , define 0ef by ( 44 ) Def = s , where gi ( a ) = f : ( a ) , аєey , 9 : ( a ) ...
Let q be a non - negative function belonging to C ( R ) , vanishing outside [ - 1 , +
1 ] , and satisfying Q ( x ) = 9 ( - x ) and Se ola ) da = 1 . For each E > 0 , and each
BEH ' , define 0ef by ( 44 ) Def = s , where gi ( a ) = f : ( a ) , аєey , 9 : ( a ) ...
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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 |