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 2020
We may therefore conclude from Theorem 7 that the natural closed extension As
of the formal differential operator ( 18 ) with An P = 0 has its spectrum o ( As ) the
whole complex plane unless A is of order zero , that is , none of its elements ...
We may therefore conclude from Theorem 7 that the natural closed extension As
of the formal differential operator ( 18 ) with An P = 0 has its spectrum o ( As ) the
whole complex plane unless A is of order zero , that is , none of its elements ...
Page 2307
Let – be a formally symmetric formal differential operator of order n defined on an
interval I . Let the deficiency indices of both be equal to an integer m . Let Aį , i = 1
, . . . , m , be a set of m linearly independent boundary values for 7 . Let S be ...
Let – be a formally symmetric formal differential operator of order n defined on an
interval I . Let the deficiency indices of both be equal to an integer m . Let Aį , i = 1
, . . . , m , be a set of m linearly independent boundary values for 7 . Let S be ...
Page 2371
... who studied the case in which linear conditions are imposed at interior points
of the interval of definition of a formal differential operator . The abstract operator -
theoretic approach via perturbation theorems used in Section 2 was introduced ...
... who studied the case in which linear conditions are imposed at interior points
of the interval of definition of a formal differential operator . The abstract operator -
theoretic approach via perturbation theorems used in Section 2 was introduced ...
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Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1929 |
Copyright | |
47 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 function 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 |