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 2325
5 and from formulas ( 16 ) and ( 14 ) . It also follows , from Lemma 3 . 5 , formula (
16 ) , and formula ( 14 ) , that the zero Én of M ( u ) in R7 has the asymptotic
representation m = 1 m = 1 Én ~ 20n + & + za + Ž Smn - m , and that the zero & n
of M ...
5 and from formulas ( 16 ) and ( 14 ) . It also follows , from Lemma 3 . 5 , formula (
16 ) , and formula ( 14 ) , that the zero Én of M ( u ) in R7 has the asymptotic
representation m = 1 m = 1 Én ~ 20n + & + za + Ž Smn - m , and that the zero & n
of M ...
Page 2341
We wish to show , using formula ( 58 ) , that the family of all sums Eml med J
ranging over all finite sets of integers , is uniformly bounded . This follows from (
58 ) by an argument using Lemma 7 , which is similar to the corresponding
argument ...
We wish to show , using formula ( 58 ) , that the family of all sums Eml med J
ranging over all finite sets of integers , is uniformly bounded . This follows from (
58 ) by an argument using Lemma 7 , which is similar to the corresponding
argument ...
Page 2347
3 . 21 ) that for each f in L2 , the set of functions 2 m - kla rld lk ( v ) ( E ( ^ m ) f ) ( t
) , PZK , m = K ( dx ) is uniformly bounded in L2 ( 0 , 1 ) . It follows from formula (
28 ) ( in Case 1A ) and from the corresponding formula ( 57 ) ( in Case 2 ) that m ...
3 . 21 ) that for each f in L2 , the set of functions 2 m - kla rld lk ( v ) ( E ( ^ m ) f ) ( t
) , PZK , m = K ( dx ) is uniformly bounded in L2 ( 0 , 1 ) . It follows from formula (
28 ) ( in Case 1A ) and from the corresponding formula ( 57 ) ( in Case 2 ) that m ...
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Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1929 |
Copyright | |
28 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 countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension fact 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 |