Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |
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Results 1-3 of 91
Page 1983
Some Examples of Bounded Spectral Operators In this section some of the
preceding results will be illustrated by considering the algebra A of all
convolution operators in H = L2 ( RN ) , the Hilbert space of square integrable
functions on real ...
Some Examples of Bounded Spectral Operators In this section some of the
preceding results will be illustrated by considering the algebra A of all
convolution operators in H = L2 ( RN ) , the Hilbert space of square integrable
functions on real ...
Page 2396
Let o4 be as in the preceding lemma , put A ( a ) = A ( Qil :; ( ) ) ) , and let B ( a ) =
A ( 04 ( :, u ( a ) ) ) ( cf. Lemma 4 for the definition of u ( a ) ) . Then , by the
preceding lemma , by Lemma 1 , and by formulas ( 2a ) and ( 2b ) , B ( A ) | ~ A ( 2
) | as ...
Let o4 be as in the preceding lemma , put A ( a ) = A ( Qil :; ( ) ) ) , and let B ( a ) =
A ( 04 ( :, u ( a ) ) ) ( cf. Lemma 4 for the definition of u ( a ) ) . Then , by the
preceding lemma , by Lemma 1 , and by formulas ( 2a ) and ( 2b ) , B ( A ) | ~ A ( 2
) | as ...
Page 2455
Therefore , if we let the three operators of the preceding lemma be H2 , H1 , H1 ,
we obtain the present corollary . Q.E.D. 5 COROLLARY . Under the hypotheses
of the preceding corollary , U ( H1 , H2 ) is an isometric mapping of E ( H1 , H2 ) ...
Therefore , if we let the three operators of the preceding lemma be H2 , H1 , H1 ,
we obtain the present corollary . Q.E.D. 5 COROLLARY . Under the hypotheses
of the preceding corollary , U ( H1 , H2 ) is an isometric mapping of E ( H1 , H2 ) ...
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Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1929 |
Copyright | |
28 other sections not shown
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adjoint operator Amer analytic apply arbitrary assumed B-space Banach space belongs Boolean algebra Borel set boundary conditions bounded bounded operator Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension fact finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear operator Math Moreover multiplicity norm perturbation plane positive preceding present problem projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type seen sequence shown shows similar solution spectral measure spectral operator spectrum subset sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero
Bibliographic information
| Title | Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 Pure and applied mathematics, v. 7 |
| Authors | Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle |
| Editors | L. Bers, J. J. Stoker |
| Publisher | Wiley-Interscience, 1957 |
| Original from | the University of Michigan |
| Digitized | 2 Feb 2010 |
| ISBN | 0471226394, 9780471226390 |
| Length | 667 pages |
| Export Citation | BiBTeX EndNote RefMan |