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 2381
If S is some other positive constant and S < € , then ag 2 ag . Let hu ( t ) , ( t , u ) € [
ag , 00 ) * Pi , be the solution of equation ( 7 ) which exists in C [ ag , oo ) , by the
above . Then , by the uniqueness of the solution of ( 7 ) , we have hu ( t ) = hult ) ...
If S is some other positive constant and S < € , then ag 2 ag . Let hu ( t ) , ( t , u ) € [
ag , 00 ) * Pi , be the solution of equation ( 7 ) which exists in C [ ag , oo ) , by the
above . Then , by the uniqueness of the solution of ( 7 ) , we have hu ( t ) = hult ) ...
Page 2391
Appropriate choice of this second solution will enable us to calculate finer
properties of the resolvent as needed below . The following corollary summarizes
the necessary facts in a form convenient for later use . 6 COROLLARY . Let Aa )
and u ...
Appropriate choice of this second solution will enable us to calculate finer
properties of the resolvent as needed below . The following corollary summarizes
the necessary facts in a form convenient for later use . 6 COROLLARY . Let Aa )
and u ...
Page 2394
solutions ởi = 0 ( t , - u ( a ) ) and ( i = 0 ; lt , ula ) ) of the equation to = do . ... Then
there exists a solution oz ( t , u ) of the equation to = u o , defined for 0 St < oo and
for all sufficiently small u e P + , such that oz and os are continuous in t and Me ...
solutions ởi = 0 ( t , - u ( a ) ) and ( i = 0 ; lt , ula ) ) of the equation to = do . ... Then
there exists a solution oz ( t , u ) of the equation to = u o , defined for 0 St < oo and
for all sufficiently small u e P + , such that oz and os are continuous in t and Me ...
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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 |