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 1915
This was possible since it concerns a type of operator with a number of special
properties including first order rate of growth of the resolvent near the spectrum .
Thus the reader whose primary interest is in the applications to such topics as ...
This was possible since it concerns a type of operator with a number of special
properties including first order rate of growth of the resolvent near the spectrum .
Thus the reader whose primary interest is in the applications to such topics as ...
Page 1931
Here and elsewhere the symbol R ( $ ; T ) is used for the resolvent ( ŠI – T ) - 1 of
T at the point & in the resolvent set p ( T ) . If x is a vector in X , then by an analytic
extension of R ( É ; T ) x will be meant an X - valued function f defined and ...
Here and elsewhere the symbol R ( $ ; T ) is used for the resolvent ( ŠI – T ) - 1 of
T at the point & in the resolvent set p ( T ) . If x is a vector in X , then by an analytic
extension of R ( É ; T ) x will be meant an X - valued function f defined and ...
Page 1933
The Resolvent of a Spectral Operator The vector valued analytic functions R ( E ;
T ' ) x associated with the resolvent of a bounded spectral operator have a
number of important properties not enjoyed by functions of the form R ( $ ; T ' ) x
when ...
The Resolvent of a Spectral Operator The vector valued analytic functions R ( E ;
T ' ) x associated with the resolvent of a bounded spectral operator have a
number of important properties not enjoyed by functions of the form R ( $ ; T ' ) x
when ...
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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 |