Linear Operators: Spectral theory |
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Page 1190
Of course if T is a bounded everywhere defined operator then the statements To
DT and T* = T are equivalent and thus a bounded operator is symmetric if and
only if it is self adjoint. If T is an everywhere defined symmetric operator then To
DT ...
Of course if T is a bounded everywhere defined operator then the statements To
DT and T* = T are equivalent and thus a bounded operator is symmetric if and
only if it is self adjoint. If T is an everywhere defined symmetric operator then To
DT ...
Page 1212
Then J. (B. of)0)f(a)(i) = s...f6)(4...F)() (d.) = s.s.)(F(T))(), (d) = s.so)(A.P)() (d.) =s. (
B.f)(A)P3)4(a) Thus, (Barif)(A) = (B,f)(A) u-almost everywhere on ea.
Consequently (B.f)(a) = s.s.)"...(s.3) (ds), feliss., , ), Aer. This fact, together with the
uniqueness ...
Then J. (B. of)0)f(a)(i) = s...f6)(4...F)() (d.) = s.s.)(F(T))(), (d) = s.so)(A.P)() (d.) =s. (
B.f)(A)P3)4(a) Thus, (Barif)(A) = (B,f)(A) u-almost everywhere on ea.
Consequently (B.f)(a) = s.s.)"...(s.3) (ds), feliss., , ), Aer. This fact, together with the
uniqueness ...
Page 1402
(t) is void, and it follows from Theorem 6.13 that W,(', 'A)e L2(a,b) u,-almost
everywhere in A. The proof of Theorem 5.4 will then apply with evident slight
modifications to show that if B(f) = 0 is a boundary condition satisfied by all fe? (T)
, we have ...
(t) is void, and it follows from Theorem 6.13 that W,(', 'A)e L2(a,b) u,-almost
everywhere in A. The proof of Theorem 5.4 will then apply with evident slight
modifications to show that if B(f) = 0 is a boundary condition satisfied by all fe? (T)
, we have ...
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Contents
SPECTRAL THEORY | 858 |
868 | 885 |
Miscellaneous Applications | 937 |
Copyright | |
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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 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 |