Linear Operators, Part 2 |
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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 , ( E ” ) . ... V +
the closure in E " 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 , ( E ” ) . ... V +
the closure in E " 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
into the set of functions vanishing on the boundary of the cube I . Next observe
that by ( 6 ) , Om S 19 = Sx0mW , so that by ( 7 ) , SL9 vanishes together with all
its first derivatives if one of x1 , . . . , xn is zero and if – k = min ( L ) Smax ( L ) Sk -
1 .
into the set of functions vanishing on the boundary of the cube I . Next observe
that by ( 6 ) , Om S 19 = Sx0mW , so that by ( 7 ) , SL9 vanishes together with all
its first derivatives if one of x1 , . . . , xn is zero and if – k = min ( L ) Smax ( L ) Sk -
1 .
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Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
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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 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 give 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
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Bibliographic information
| Title | Linear Operators, Part 2 Linear Operators, Jacob T. Schwartz Volume 7 of Pure and applied mathematics Issue 7 of Pure and applied mathematics; a series of monographs and textbooks |
| Authors | Nelson Dunford, Jacob T. Schwartz |
| Publisher | Interscience Publishers, 1963 |
| Original from | the University of Michigan |
| Digitized | 20 Nov 2007 |
| ISBN | 0471226386, 9780471226383 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |