Linear Operators: General theory |
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Page 365
Show that the map : f f defined in Exercise 53 maps H , in a linear one - one manner onto the closed subspace of Lo consisting of those F all of whose negative Fourier coefficients vanish . 55 Using the notations of Exercises 53 and 54 ...
Show that the map : f f defined in Exercise 53 maps H , in a linear one - one manner onto the closed subspace of Lo consisting of those F all of whose negative Fourier coefficients vanish . 55 Using the notations of Exercises 53 and 54 ...
Page 371
( Hint : Generalize the argument of Exercise 85 to apply to zeros on the boundary of the unit disc . ) 88 Show that Exercise 87 is valid even if p = 1 . 89 Every function f in H , can be written as a product gh , where y and h are in H.
( Hint : Generalize the argument of Exercise 85 to apply to zeros on the boundary of the unit disc . ) 88 Show that Exercise 87 is valid even if p = 1 . 89 Every function f in H , can be written as a product gh , where y and h are in H.
Page 531
This is the vector form of Exercise 6. ) C. Inequalities of Hardy - Hilbert type . The next set of inequalities are all variations on the surprisingly simple theme given in Exercise 15 , which lends itself to surprisingly manifold ...
This is the vector form of Exercise 6. ) C. Inequalities of Hardy - Hilbert type . The next set of inequalities are all variations on the surprisingly simple theme given in Exercise 15 , which lends itself to surprisingly manifold ...
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
quences | 26 |
Copyright | |
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Common terms and phrases
Akad algebra Amer analytic applied arbitrary assume B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math mean measure space metric space neighborhood norm o-field open set operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology transformations u-integrable u-measurable uniformly union unique unit valued vector weak zero
Bibliographic information
| Title | Linear Operators: General theory Part 1 of Linear Operators, Jacob T. Schwartz Volume 1 of Linear Operators: General Theory. Spectral Theory, Self Adjoint Operators in Hilbert Space. Spectral Operators. I. II. III, William George Bade Volume 7 of Pure & Applied Mathematics : a Wiley-interscience series of texts, monographs & tracts Volume 7 of Pure and applied mathematics : a series of texts and monographs Volume 7 of Pure and applied mathematics Interscience Press Pure and applied mathematics, ISSN 0079-8185 Wiley classics library |
| Authors | Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle |
| Editors | William G. Bade, Robert G. Bartle |
| Contributor | Karreman Mathematics Research Collection |
| Edition | reprint |
| Publisher | Interscience Publishers, 1958 |
| Original from | the University of California |
| Digitized | 16 Mar 2011 |
| ISBN | 0470226056, 9780470226056 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |