Linear Operators: Spectral theory |
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Page 1428
Then im is infinitely differentiable , and vanishes together with its derivatives for t
< 0 and for t > m . Furthermore , I ' m coincides with f for 1 < t < m - 1 , and hence
the function tim - 1 ) is identically zero in t except on the intervals m - 1 st sm and
...
Then im is infinitely differentiable , and vanishes together with its derivatives for t
< 0 and for t > m . Furthermore , I ' m coincides with f for 1 < t < m - 1 , and hence
the function tim - 1 ) is identically zero in t except on the intervals m - 1 st sm and
...
Page 1687
6 that every derivative of h ; F of order not more than k belongs to L ( En ) . ... in V
the closure in En of whose support is disjoint from the curved boundary of V + ,
and all of whose derivatives of order at most k belong to L ( V ) by Lemmas 3 .
6 that every derivative of h ; F of order not more than k belongs to L ( En ) . ... in V
the closure in En of whose support is disjoint from the curved boundary of V + ,
and all of whose derivatives of order at most k belong to L ( V ) by Lemmas 3 .
Page 1727
In the same way we see , using ( 6 ) and ( 7 ) , that SL9 vanishes together with all
its derivatives of order at most ; if one of x1 , . . . , Xn is zero and - k 5 min ( L ) S
max ( L ) Sk - j . It follows that if Tlg is defined by TL9 = SL9 | 1 , then T ' , maps ...
In the same way we see , using ( 6 ) and ( 7 ) , that SL9 vanishes together with all
its derivatives of order at most ; if one of x1 , . . . , Xn is zero and - k 5 min ( L ) S
max ( L ) Sk - j . It follows that if Tlg is defined by TL9 = SL9 | 1 , then T ' , maps ...
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Contents
IX | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Compact Groups | 945 |
Copyright | |
46 other sections not shown
Other editions - View all
Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |
Common terms and phrases
additive adjoint operator algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently consider constant contains continuous converges Corollary corresponding defined Definition denote dense derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function 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 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 Interscience Press Volume 7 of Pure and applied mathematics Wiley Classics Library |
| Authors | Nelson Dunford, Jacob T. Schwartz |
| Contributor | Karreman Mathematics Research Collection |
| Publisher | Interscience Publishers, 1963 |
| Original from | the University of Michigan |
| Digitized | 20 Nov 2007 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |