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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Page 1998
... H by equation ( 28 ) form a commuiative B * - algebra of operators in H which is
* - equivalent to the B * - algebra L . ( RM ) . The following examples are among
the most familiar convolutions in A . 11 EXAMPLE ( Translation ) . Let 14 ( 0 ) = 1
...
... H by equation ( 28 ) form a commuiative B * - algebra of operators in H which is
* - equivalent to the B * - algebra L . ( RM ) . The following examples are among
the most familiar convolutions in A . 11 EXAMPLE ( Translation ) . Let 14 ( 0 ) = 1
...
Page 1999
The preceding example shows that f * 9 = 9 + 9 = 15 ( 5 ) e ( ds ) is in L , and thus
7 ( f * p ) = [ p ( s ) re ( ds ) } = ( ( 9 ) u ( ds ) | = jõ = 5 F ( S ) u ( ds ) which shows
that f * 9 = S 5 ( ) e ( ds ) . By using a sequence { on } in Lin L , to approach an ...
The preceding example shows that f * 9 = 9 + 9 = 15 ( 5 ) e ( ds ) is in L , and thus
7 ( f * p ) = [ p ( s ) re ( ds ) } = ( ( 9 ) u ( ds ) | = jõ = 5 F ( S ) u ( ds ) which shows
that f * 9 = S 5 ( ) e ( ds ) . By using a sequence { on } in Lin L , to approach an ...
Page 2591
10.6 (1977) examples of, XV. 11 (1983) operational calculus for, XV. 10. 11 (1980
) resolutions of the identity for, XV. 10- .6(1977), XV.10.3 (1972) scalar and
radical parts of, XV. 10. 9 (1979) in 91 ' , conditions for, XV.l 1 .1 8, XV.11.19.XV.
11.20 ...
10.6 (1977) examples of, XV. 11 (1983) operational calculus for, XV. 10. 11 (1980
) resolutions of the identity for, XV. 10- .6(1977), XV.10.3 (1972) scalar and
radical parts of, XV. 10. 9 (1979) in 91 ' , conditions for, XV.l 1 .1 8, XV.11.19.XV.
11.20 ...
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Contents
SPECTRAL OPERATORS XV Spectral Operators | 1924 |
Introduction | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
32 other sections not shown
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Common terms and phrases
analytic apply arbitrary assumed B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded Borel bounded operator Chapter clear clearly closure commuting compact complex consider constant contained converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established example exists extension fact finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm positive preceding present problem projections PROOF properties prove range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows spectral measure spectral operator spectrum statement strongly subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly 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 |