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 2051
We next consider the problem of finding the explicit form of the solution to the
Cauchy problem whose existence is established in Theorem 19 . As before , we
assume that aạt > 0 . It follows from equation ( 55 ) which gives the analytical ...
We next consider the problem of finding the explicit form of the solution to the
Cauchy problem whose existence is established in Theorem 19 . As before , we
assume that aạt > 0 . It follows from equation ( 55 ) which gives the analytical ...
Page 2409
( a ) Instead of considering , as above , the space L2 ( D ) of complex valued
Lebesgue measurable functions defined in D and satisfying ( 7 ) , we may let X
be an arbitrary complex B - space , and can consider the space L ( D , X ) of X -
valued ...
( a ) Instead of considering , as above , the space L2 ( D ) of complex valued
Lebesgue measurable functions defined in D and satisfying ( 7 ) , we may let X
be an arbitrary complex B - space , and can consider the space L ( D , X ) of X -
valued ...
Page 2488
( e ) Prove that if A is an operator of the Hilbert - Schmidt class , while we Lac ( H )
and | | w | ln < 00 , then * | Aet Hv12 dt $ 217 | | A | 13 | | | * · ( Hint : Consider A self
adjoint , and expand in the eigenvectors of A . ) 17 ( a ) Let f be a continuous ...
( e ) Prove that if A is an operator of the Hilbert - Schmidt class , while we Lac ( H )
and | | w | ln < 00 , then * | Aet Hv12 dt $ 217 | | A | 13 | | | * · ( Hint : Consider A self
adjoint , and expand in the eigenvectors of A . ) 17 ( a ) Let f be a continuous ...
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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 |