Linear Operators: Spectral theory |
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Page 1469
Thus statement ( a ) follows immediately from the preceding lemma . To prove
statement ( b ) , note that t is finite below 2o , but not below any 2 > ho . Statement
( b ) then follows immediately from the preceding lemma . Q . E . D . Next we turn
...
Thus statement ( a ) follows immediately from the preceding lemma . To prove
statement ( b ) , note that t is finite below 2o , but not below any 2 > ho . Statement
( b ) then follows immediately from the preceding lemma . Q . E . D . Next we turn
...
Page 1653
Statement ( iii ) follows from statement ( ii ) and the fact that Flu + 1 2 Flu ) for all k
20 and Fin H ( + 1 ) ( I ) , ( cf . Definition 15 ( i ) ) . To prove ( ii ) and the final
statement of the lemma , we first note that it is evident for k 2 0 from Definition 15 (
i ) .
Statement ( iii ) follows from statement ( ii ) and the fact that Flu + 1 2 Flu ) for all k
20 and Fin H ( + 1 ) ( I ) , ( cf . Definition 15 ( i ) ) . To prove ( ii ) and the final
statement of the lemma , we first note that it is evident for k 2 0 from Definition 15 (
i ) .
Page 1756
( B ) The uniqueness of the function V of the theorem is an evident consequence
of statement ( i ) . Moreover , statement ( i ) enables us to reduce the proof of the
existence of the function V to the proof of the following statement . ( ii ) For each r
...
( B ) The uniqueness of the function V of the theorem is an evident consequence
of statement ( i ) . Moreover , statement ( i ) enables us to reduce the proof of the
existence of the function V to the proof of the following statement . ( ii ) For each r
...
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Contents
BAlgebras | 859 |
Commutative BAlgebras | 869 |
Commutative BAlgebras | 877 |
Copyright | |
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additive adjoint adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure coefficients commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension fact finite follows formal differential operator formula function function f give given Hence Hilbert space ideal identity independent indices inequality integral interval isometric isomorphism Lemma linear mapping matrix measure multiplicity neighborhood norm normal operator obtained positive preceding present projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique unit vanishes vector zero
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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, 1963 |
| Original from | the University of Michigan |
| Digitized | 20 Nov 2007 |
| ISBN | 0470226382, 9780470226384 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |