Linear Operators, Part 2 |
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Page 1662
Then the closed set Cg in I , which is the complement of the largest open set in I
in which F vanishes , i . e . , which is the complement in I of the union of all the
open subsets of I in which F vanishes , is called the carrier of F . Lemma 12 now ...
Then the closed set Cg in I , which is the complement of the largest open set in I
in which F vanishes , i . e . , which is the complement in I of the union of all the
open subsets of I in which F vanishes , is called the carrier of F . Lemma 12 now ...
Page 1663
for each open subset 1 . of I whose closure is compact and contained in I . 35
DEFINITION . Let I be an open subset of C and let k be a positive integer . ( i ) The
set of all F in D , ( I ) for which \ F ( q ) ) < co | Fli _ k ) = sup DEC 0 ( 1 ) 1911 ) will
...
for each open subset 1 . of I whose closure is compact and contained in I . 35
DEFINITION . Let I be an open subset of C and let k be a positive integer . ( i ) The
set of all F in D , ( I ) for which \ F ( q ) ) < co | Fli _ k ) = sup DEC 0 ( 1 ) 1911 ) will
...
Page 1696
By Lemma 14 there is a sequence { Fm } of elements of D ( I ) , each of which has
a carrier which is a compact subset C of I , and such that Fm → F as m → 00 .
Hence , we can evidently suppose without loss of generality that the carrier C of F
...
By Lemma 14 there is a sequence { Fm } of elements of D ( I ) , each of which has
a carrier which is a compact subset C of I , and such that Fm → F as m → 00 .
Hence , we can evidently suppose without loss of generality that the carrier C of F
...
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Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
57 other sections not shown
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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 |