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 2307
The last example above illustrates a problem which will be of great concern to us
in the remainder of this chapter : the problem of finding which formal differential
operators and sets of boundary conditions lead to spectral operators . As our ...
The last example above illustrates a problem which will be of great concern to us
in the remainder of this chapter : the problem of finding which formal differential
operators and sets of boundary conditions lead to spectral operators . As our ...
Page 2350
But , under the condition that the set of boundary conditions Ci ( Uf ) = 0 is regular
, this has been established above . Thus , to complete the proof , it suffices to
show that the set of boundary conditions Ci ( Uf ) = 0 , i = 1 , ... , n , is regular .
But , under the condition that the set of boundary conditions Ci ( Uf ) = 0 is regular
, this has been established above . Thus , to complete the proof , it suffices to
show that the set of boundary conditions Ci ( Uf ) = 0 , i = 1 , ... , n , is regular .
Page 2371
Birkhoff [ 3 ] showed that if the set of boundary conditions is subject to the
regularity hypotheses of Section 4 , the eigenvalue expansion of a function f of
bounded variation converges to i { f ( t + 0 ) + f ( t - 0 ) } at an interior point t of the
interval ...
Birkhoff [ 3 ] showed that if the set of boundary conditions is subject to the
regularity hypotheses of Section 4 , the eigenvalue expansion of a function f of
bounded variation converges to i { f ( t + 0 ) + f ( t - 0 ) } at an interior point t of the
interval ...
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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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Common terms and phrases
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 |