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 1917
If an unperturbed operator T and a perturbed operator T ” derived from it are both
self adjoint , then a non - rigorous formal argument can be used to buttress the
expectation that the Friedrichs operator U realizing the similarity UTU - 1 = T ...
If an unperturbed operator T and a perturbed operator T ” derived from it are both
self adjoint , then a non - rigorous formal argument can be used to buttress the
expectation that the Friedrichs operator U realizing the similarity UTU - 1 = T ...
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 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 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 |