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 |
From inside the book
Results 1-3 of 41
Page 2381
Now define oi ( t , x ) to be the unique solution of ( T - u ? ) o = 0 , ( t , u ) [ 0 , 0 ) < Pt , which coincides with gu ( t ) for t 2 a . ( cf. Corollary XIII.1.5 ) . If S is some other positive constant and 8 < , then ag 2 Qe .
Now define oi ( t , x ) to be the unique solution of ( T - u ? ) o = 0 , ( t , u ) [ 0 , 0 ) < Pt , which coincides with gu ( t ) for t 2 a . ( cf. Corollary XIII.1.5 ) . If S is some other positive constant and 8 < , then ag 2 Qe .
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 ” oz ( t ...
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 ” oz ( t ...
Page 2394
λσ a - solutions ởi = gilt , -u ( a ) ) and on = oit , u ( a ) ) of the equation to = do . ... Then there exists a solution og ( t , ) of the equation to ru'o , defined for 0 St < oo and oz , u = for all sufficiently small ue P + ...
λσ a - solutions ởi = gilt , -u ( a ) ) and on = oit , u ( a ) ) of the equation to = do . ... Then there exists a solution og ( t , ) of the equation to ru'o , defined for 0 St < oo and oz , u = for all sufficiently small ue P + ...
What people are saying - Write a review
We haven't found any reviews in the usual places.
Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1929 |
Copyright | |
31 other sections not shown
Other editions - View all
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 gives 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 |