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 2017
As another example , consider the formal differential operator 22 -ai as ; ( 14 ) 22 Bi as where a , ß are positive real numbers . If a #B , the corresponding closed operator As cannot be self adjoint , but it always has a resolution of ...
As another example , consider the formal differential operator 22 -ai as ; ( 14 ) 22 Bi as where a , ß are positive real numbers . If a #B , the corresponding closed operator As cannot be self adjoint , but it always has a resolution of ...
Page 2020
We may there- . fore conclude from Theorem 7 that the natural closed extension As of the formal differential operator ( 18 ) with A " ØP = 0 has its spectrum o ( As ) the whole complex plane unless A is of order zero , that is , none of ...
We may there- . fore conclude from Theorem 7 that the natural closed extension As of the formal differential operator ( 18 ) with A " ØP = 0 has its spectrum o ( As ) the whole complex plane unless A is of order zero , that is , none of ...
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 ...
... 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 ...
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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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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 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 |