Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 66
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 ( 1 ) , each of which
has a carrier which is a compact subset Cm of I , and such that Fm → F as m →
00 . Hence , we can evidently suppose without loss of generality that the carrier C
of ...
By Lemma 14 there is a sequence { Fm } of elements of D ( 1 ) , each of which
has a carrier which is a compact subset Cm of I , and such that Fm → F as m →
00 . Hence , we can evidently suppose without loss of generality that the carrier C
of ...
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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 |