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 1983
... all convolution operators in H = L2 ( RN ) , the Hilbert space of square
integrable functions on real Euclidean space RN of ... countably additive set
functions , ordinary Lebesgue integrals , proper value integrals or any other
improper integral ...
... all convolution operators in H = L2 ( RN ) , the Hilbert space of square
integrable functions on real Euclidean space RN of ... countably additive set
functions , ordinary Lebesgue integrals , proper value integrals or any other
improper integral ...
Page 2042
1 ) we have , by differentiating under the integral sign as before , RN RN ( 241o , )
( Q ) = Sxv6 – 1 « la za ( F - 14 ) ... ( s ) in the preceding integrand is square
integrable on RN and the same is true of its Fourier transform F ( ( - 1 ) | a1 ( 2 . ) ...
1 ) we have , by differentiating under the integral sign as before , RN RN ( 241o , )
( Q ) = Sxv6 – 1 « la za ( F - 14 ) ... ( s ) in the preceding integrand is square
integrable on RN and the same is true of its Fourier transform F ( ( - 1 ) | a1 ( 2 . ) ...
Page 2043
... is continuous on RN and square integrable on RN , then q belongs to D ( A ) .
21 THEOREM . Using the notation of Theorem 19 and letting B be an arbitrary
bounded linear operator in HP , we have : ( i ) The operator As + B with domain D
...
... is continuous on RN and square integrable on RN , then q belongs to D ( A ) .
21 THEOREM . Using the notation of Theorem 19 and letting B be an arbitrary
bounded linear operator in HP , we have : ( i ) The operator As + B with domain D
...
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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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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 |