Linear Operators: Spectral operators |
From inside the book
Results 1-3 of 91
Page 2025
Since Ex : ( s ) # 0 there is a vector f ( s ) in EP with \ ¥ ( s ) = 1 and ( s ) = Êxj ( s ) (
s ) . Thus , since Êx ; ( s ) and Êxg ( s ) are disjoint projections if q # j , it follows
from ( 35 ) that R ( a ; Â ( s ) ) " } ( s ) = 4 ( s ) ( 1 - dxy ( s ) ) - - and ( 39 ) gives -
Axy ...
Since Ex : ( s ) # 0 there is a vector f ( s ) in EP with \ ¥ ( s ) = 1 and ( s ) = Êxj ( s ) (
s ) . Thus , since Êx ; ( s ) and Êxg ( s ) are disjoint projections if q # j , it follows
from ( 35 ) that R ( a ; Â ( s ) ) " } ( s ) = 4 ( s ) ( 1 - dxy ( s ) ) - - and ( 39 ) gives -
Axy ...
Page 2031
To prove ( iv ) suppose first that ys is in 0 in which case a permissible interchange
of integration gives RN RN ( FT . ) q ) = S ( Fp ) ( $ ) { ( 8 ) ds = S 968 ) ( F % ) ( 3 )
ds = Trulm ) , de D . Now 0 is dense in H = L2 ( RN ) and thus there is for an ...
To prove ( iv ) suppose first that ys is in 0 in which case a permissible interchange
of integration gives RN RN ( FT . ) q ) = S ( Fp ) ( $ ) { ( 8 ) ds = S 968 ) ( F % ) ( 3 )
ds = Trulm ) , de D . Now 0 is dense in H = L2 ( RN ) and thus there is for an ...
Page 2065
Thus the Gelfand theory gives a general procedure for determining whether or
not an element possesses an inverse and so ... In order to apply this procedure to
a given algebra , it is sufficient to give a satisfactory representation of its spectrum
...
Thus the Gelfand theory gives a general procedure for determining whether or
not an element possesses an inverse and so ... In order to apply this procedure to
a given algebra , it is sufficient to give a satisfactory representation of its spectrum
...
What people are saying - Write a review
We haven't found any reviews in the usual places.
Other editions - View all
Common terms and phrases
algebra of projections analytic apply arbitrary assumed B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded Borel bounded operator Chapter clear closure commuting compact complete 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 formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm normal 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 strongly subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero
Bibliographic information
| Title | Linear Operators: Spectral operators Part 3 of Linear Operators, Jacob T. Schwartz Volume 7 of Pure & Applied Mathematics : a Wiley-interscience series of texts, monographs & tracts Volume 7 of Pure and applied mathematics : a series of texts and monographs Volume 7 of Pure and applied mathematics Interscience Press Pure and applied mathematics, ISSN 0079-8185 Wiley classics library |
| Authors | Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle |
| Editors | William G. Bade, Robert G. Bartle |
| Contributor | Karreman Mathematics Research Collection |
| Edition | reprint |
| Publisher | Interscience Publishers, 1958 |
| ISBN | 0471226394, 9780471226390 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |