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 1940
8 that S is uniquely determined by T . Hence N = T - S is uniquely determined by
T . It follows from Lemma 4 that T and S have the same spectrum . Next it will be
shown that every spectral operator T has the desired decomposition .
8 that S is uniquely determined by T . Hence N = T - S is uniquely determined by
T . It follows from Lemma 4 that T and S have the same spectrum . Next it will be
shown that every spectral operator T has the desired decomposition .
Page 2029
As an example of a tempered distribution we might mention the function T ,
determined by a bounded finitely additive ... pe D . Similarly , functions on RN
may determine tempered distributions just as they sometimes determine
distributions .
As an example of a tempered distribution we might mention the function T ,
determined by a bounded finitely additive ... pe D . Similarly , functions on RN
may determine tempered distributions just as they sometimes determine
distributions .
Page 2373
which exclude the whole complex plane from the spectrum of the operator they
determine . ... These boundary conditions determine discrete differential
operators having eigenvalues d = 82 determined by equations of the form sin 8 =
ks .
which exclude the whole complex plane from the spectrum of the operator they
determine . ... These boundary conditions determine discrete differential
operators having eigenvalues d = 82 determined by equations of the form sin 8 =
ks .
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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 |