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
Now define o ( t , u ) to be the unique solution of ( r - u ? ) o = 0 , ( t , u ) € [ 0 , 0 ) < Pet , which coincides with gult ) for t 2 az ( cf. Corollary XIII.1.5 ) . If S is some other positive constant and S < € , then ag 2 ag .
Now define o ( t , u ) to be the unique solution of ( r - u ? ) o = 0 , ( t , u ) € [ 0 , 0 ) < Pet , which coincides with gult ) for t 2 az ( cf. Corollary XIII.1.5 ) . If S is some other positive constant and S < € , then ag 2 ag .
Page 2384
Q.E.D. For the spectral analysis of the operator T , we shall also need asymptotic information on the “ second solution ” of the differential equation To to = użo , that is , the solution asymptotic to e - tut as t + 00 .
Q.E.D. For the spectral analysis of the operator T , we shall also need asymptotic information on the “ second solution ” of the differential equation To to = użo , that is , the solution asymptotic to e - tut as t + 00 .
Page 2391
For use in what is to follow we record the formula for R ( a ; T ' ) obtained in the proof of Lemma 4 and also observe that in constructing the kernel R ( s , t ; d ) in Lemma 4 we may replace the particular “ second solution " ozlt ...
For use in what is to follow we record the formula for R ( a ; T ' ) obtained in the proof of Lemma 4 and also observe that in constructing the kernel R ( s , t ; d ) in Lemma 4 we may replace the particular “ second solution " ozlt ...
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Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1929 |
Copyright | |
47 other sections not shown
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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 defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension 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 |