Linear Operators: Spectral theory |
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Page 910
This shows that U , preserves inner products and is thus one - to - one and
continuous . It therefore has a unique extension U from Di = H to the L , - closure
of the set of bounded Borel functions , i . e . , to L , ( u ) . An elementary continuity
...
This shows that U , preserves inner products and is thus one - to - one and
continuous . It therefore has a unique extension U from Di = H to the L , - closure
of the set of bounded Borel functions , i . e . , to L , ( u ) . An elementary continuity
...
Page 985
Let F be a continuous linear functional on L ( R ) which vanishes on L , let o be
the bounded measurable function representing F ( IV . 8 . 5 ) , and let f be any
point in L . Then , since 0 = F ) , = SRP ( x ) / ( x − y ) dx equation ( i ) shows that F
...
Let F be a continuous linear functional on L ( R ) which vanishes on L , let o be
the bounded measurable function representing F ( IV . 8 . 5 ) , and let f be any
point in L . Then , since 0 = F ) , = SRP ( x ) / ( x − y ) dx equation ( i ) shows that F
...
Page 987
The preceding theorem shows that there is a point mo in Ř with h ( mo ) = 0 for
every h in L . Furthermore , since t is closed in the L ( R ) topology of L ( R ) , it
follows from Corollary V . 3 . 12 that A is the conjugate - orthogonal complement
of L ...
The preceding theorem shows that there is a point mo in Ř with h ( mo ) = 0 for
every h in L . Furthermore , since t is closed in the L ( R ) topology of L ( R ) , it
follows from Corollary V . 3 . 12 that A is the conjugate - orthogonal complement
of L ...
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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 |