Linear Operators: Spectral theory |
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Page 1211
... of S and the real number system R which is measurable with respect to the
product of v and the measure u = (E(-)g, g), and which has the property that for
every bounded Borel set e of reals and every F in L2(u) we have (i) 19-ess ops |
W(s, ...
... of S and the real number system R which is measurable with respect to the
product of v and the measure u = (E(-)g, g), and which has the property that for
every bounded Borel set e of reals and every F in L2(u) we have (i) 19-ess ops |
W(s, ...
Page 1218
The following lemma is, in the case of scalar functions, a well known theorem of
Lusin. 17 LEMMA. Let u be a finite positive regular measure on the Borel sets of a
topological space R. Then, for every B-space valued u-measurable function f on ...
The following lemma is, in the case of scalar functions, a well known theorem of
Lusin. 17 LEMMA. Let u be a finite positive regular measure on the Borel sets of a
topological space R. Then, for every B-space valued u-measurable function f on ...
Page 1221
Thus a, is the intersection of a sequence of measurable sets, and it follows that o,
is u-measurable, completing the proof of statement (i). To complete the proof of
the theorem, suppose that the functions Wi(., A), ..., W,(., A) are not linearly ...
Thus a, is the intersection of a sequence of measurable sets, and it follows that o,
is u-measurable, completing the proof of statement (i). To complete the proof of
the theorem, suppose that the functions Wi(., A), ..., W,(., A) are not linearly ...
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Contents
SPECTRAL THEORY | 858 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
34 other sections not shown
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additive Akad algebra Amer analytic applied assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complete 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 measure multiplicity neighborhood norm obtained partial positive preceding present problem projection PRoof properties prove range regular remark representation respectively restriction result satisfies seen sequence 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 |
| ISBN | 0470226382, 9780470226384 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |