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 1930
If Eis a Boolean algebra of subsets of the complex plane which contains the void set and the whole plane , in short , if & is a field of sets in the complex plane , then a spectral measure E on is called a resolution of the identity ...
If Eis a Boolean algebra of subsets of the complex plane which contains the void set and the whole plane , in short , if & is a field of sets in the complex plane , then a spectral measure E on is called a resolution of the identity ...
Page 2043
The semi - group S ( t ) has a strongly analytic extension to a semi - group S ( ) defined for 5 in the half plane R ( S ) > 0 . The unique solution to the Cauchy problem presented by the equations ( ii ) , ( iii ) , ( iv ) is analytic ...
The semi - group S ( t ) has a strongly analytic extension to a semi - group S ( ) defined for 5 in the half plane R ( S ) > 0 . The unique solution to the Cauchy problem presented by the equations ( ii ) , ( iii ) , ( iv ) is analytic ...
Page 2087
... the infinitesimal generator of a strongly continuous semi - group S ( t ) , t 2 0 , of bounded linear operators in HP and S ( t ) has a strongly analytic extension to a semi - group S ( ) defined for in the half plane R ( $ ) > 0 .
... the infinitesimal generator of a strongly continuous semi - group S ( t ) , t 2 0 , of bounded linear operators in HP and S ( t ) has a strongly analytic extension to a semi - group S ( ) defined for in the half plane R ( $ ) > 0 .
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Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1929 |
Copyright | |
31 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 contained continuous converges Corollary corresponding defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension finite follows formal formula function given Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear 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 |