Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 84
Page 984
The set of functions f in Ly ( R ) for which s vanishes in a neighborhood of infinity
is dense in Ly ( R ) . Proof . It follows from Lemma 3 . 6 that the set of all functions
in L2 ( R , B , u ) which vanish outside of compact sets is dense in this space ...
The set of functions f in Ly ( R ) for which s vanishes in a neighborhood of infinity
is dense in Ly ( R ) . Proof . It follows from Lemma 3 . 6 that the set of all functions
in L2 ( R , B , u ) which vanish outside of compact sets is dense in this space ...
Page 993
It remains to be proved that the number ay is independent of the open set V . If f is
in Lj ( R ) L2 ( R ) , f vanishes on the complement of V , and f ( m ) = 1 for m in an
open subset V , of V , then the above proof shows that ( 0f ) ( m ) = Qy for every ...
It remains to be proved that the number ay is independent of the open set V . If f is
in Lj ( R ) L2 ( R ) , f vanishes on the complement of V , and f ( m ) = 1 for m in an
open subset V , of V , then the above proof shows that ( 0f ) ( m ) = Qy for every ...
Page 997
Since of is in L ( R ) , L ( R ) whenever f is , it follows that Ø maps each function in
L ( R ) , L ( R ) into a continuous function on R which vanishes at Poo . 23
THEOREM . Let y be a bounded measurable function on R . Then a point m , in Ř
is in ...
Since of is in L ( R ) , L ( R ) whenever f is , it follows that Ø maps each function in
L ( R ) , L ( R ) into a continuous function on R which vanishes at Poo . 23
THEOREM . Let y be a bounded measurable function on R . Then a point m , in Ř
is in ...
What people are saying - Write a review
We haven't found any reviews in the usual places.
Contents
IX | 859 |
Eigenvalues and Eigenvectors | 903 |
Spectral Representation | 911 |
Copyright | |
15 other sections not shown
Other editions - View all
Common terms and phrases
additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result Russian satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero
Bibliographic information
| Title | Linear Operators: Spectral theory Part 2 of Linear Operators, Jacob T. Schwartz Volume 7 of Pure and applied mathematics : a series of texts and monographs Volume 7 of Pure and applied mathematics Interscience Press Volume 7 of Pure and applied mathematics Wiley Classics Library |
| Authors | Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle |
| Contributor | Karreman Mathematics Research Collection |
| Publisher | Interscience Publishers, 1958 |
| Original from | the University of Michigan |
| Digitized | 2 Feb 2010 |
| ISBN | 0470226382, 9780470226384 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |