Linear Operators: Spectral theory |
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Page 995
If y and f are in L ( R ) and L ( R ) respectively and if f ( m ) = 0 for every m in the
spectral set o ( 9 ) , then olf * ) contains no isolated points ... Let h be in L ( R )
with ħ ( mo ) = 1 and ħ vanishing on an open set containing the remainder of olf *
p ) .
If y and f are in L ( R ) and L ( R ) respectively and if f ( m ) = 0 for every m in the
spectral set o ( 9 ) , then olf * ) contains no isolated points ... Let h be in L ( R )
with ħ ( mo ) = 1 and ħ vanishing on an open set containing the remainder of olf *
p ) .
Page 996
From Lemma 12 ( b ) it is seen that olf * ) Colp ) and from Lemma 12 ( c ) and the
equation of = tf it follows that olf * 9 ) contains no interior point of o ( 9 ) . Hence of
* ) is a closed subset of the boundary of o ( q ) . Since f * 9 = 0 it follows from ...
From Lemma 12 ( b ) it is seen that olf * ) Colp ) and from Lemma 12 ( c ) and the
equation of = tf it follows that olf * 9 ) contains no interior point of o ( 9 ) . Hence of
* ) is a closed subset of the boundary of o ( q ) . Since f * 9 = 0 it follows from ...
Page 1456
Suppose for definiteness that I contains a neighborhood of the left end point a of I
, so that , unless I1 = I ( in which case t = t , and is evidently bounded below ) , I ,
contains a neighborhood of the right end point b of 1 . Unless 12 = I , in which ...
Suppose for definiteness that I contains a neighborhood of the left end point a of I
, so that , unless I1 = I ( in which case t = t , and is evidently bounded below ) , I ,
contains a neighborhood of the right end point b of 1 . Unless 12 = I , in which ...
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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 |