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 39
Page 2381
Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob
Theodore Schwartz. of ( 7 ) is necessarily unique for u € P + . Now define o lt , u )
to be the unique solution of ( T - u ? ) o = 0 , ( t , u ) € [ 0 , 0 ) X Pot , which ...
Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob
Theodore Schwartz. of ( 7 ) is necessarily unique for u € P + . Now define o lt , u )
to be the unique solution of ( T - u ? ) o = 0 , ( t , u ) € [ 0 , 0 ) X Pot , which ...
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 =
u o , that is , the solution asymptotic to e - tut as t→00 . Since , in contrast to 01 ,
such a ...
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 =
u o , that is , the solution asymptotic to e - tut as t→00 . Since , in contrast to 01 ,
such a ...
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 A ( a )
and ...
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 A ( a )
and ...
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 | |
28 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 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 |