Linear Operators: Spectral theory |
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Page 889
... of disjoint Borel sets ( v ) SED , E ( 8 ) x = E ( US ; ) x , EH . i = 1 A spectral
measure E defined on the Borel sets in the plane and satisfying ( iv ) for every
Borel set d and ( v ) for every sequence { d ; } of disjoint Borel sets is called a
resolution ...
... of disjoint Borel sets ( v ) SED , E ( 8 ) x = E ( US ; ) x , EH . i = 1 A spectral
measure E defined on the Borel sets in the plane and satisfying ( iv ) for every
Borel set d and ( v ) for every sequence { d ; } of disjoint Borel sets is called a
resolution ...
Page 958
Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. ylez ) and
that E ( e ) yley ) = 0 if e , and e , are disjoint . Thus y ( e , ) and ( ez ) are
orthogonal whenever e , and e , are disjoint . Hence if e , and eg are disjoint then
yley u ...
Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. ylez ) and
that E ( e ) yley ) = 0 if e , and e , are disjoint . Thus y ( e , ) and ( ez ) are
orthogonal whenever e , and e , are disjoint . Hence if e , and eg are disjoint then
yley u ...
Page 1151
R = Un _ K . We observe that if A and B are disjoint closed subsets of R and if n is
an integer , then there is an open set U CR such that An K , CU and U n B = $ .
This is true since for each pe An Kn there is an open set U ( p ) such that pe U ( p
) ...
R = Un _ K . We observe that if A and B are disjoint closed subsets of R and if n is
an integer , then there is an open set U CR such that An K , CU and U n B = $ .
This is true since for each pe An Kn there is an open set U ( p ) such that pe U ( p
) ...
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Contents
IX | 859 |
Eigenvalues and Eigenvectors | 903 |
Spectral Representation | 911 |
Copyright | |
15 other sections not shown
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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 |