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 2325
5 and from formulas ( 16 ) and ( 14 ) . It also follows , from Lemma 3 . 5 , formula (
16 ) , and formula ( 14 ) , that the zero Šr of M ( u ) in Rom has the asymptotic
representation m = 1 m = 1 $ * ~ 2mn + & + 22 + Smu - m , and that the zero Šn of
M ...
5 and from formulas ( 16 ) and ( 14 ) . It also follows , from Lemma 3 . 5 , formula (
16 ) , and formula ( 14 ) , that the zero Šr of M ( u ) in Rom has the asymptotic
representation m = 1 m = 1 $ * ~ 2mn + & + 22 + Smu - m , and that the zero Šn of
M ...
Page 2334
On the other hand , it follows from the asymptotic formula ( 26 ) and from the
formula ( 21 ) giving the form of the kernel defining the operator Gu that if we
excise from the angle A of the u - plane ( defined by formula ( 8 ) ) a circle of
radius ε ...
On the other hand , it follows from the asymptotic formula ( 26 ) and from the
formula ( 21 ) giving the form of the kernel defining the operator Gu that if we
excise from the angle A of the u - plane ( defined by formula ( 8 ) ) a circle of
radius ε ...
Page 2340
It follows immediately from formulas ( 52 ) and ( 34 ) that ( B , Guf ) can be written
in the form ( 55 ) ( B , Gus ) = - n Tex ( de ) ... Moreover , formula ( 56 ) may clearly
be differentiated any number of times with respect to x , and still remain a valid ...
It follows immediately from formulas ( 52 ) and ( 34 ) that ( B , Guf ) can be written
in the form ( 55 ) ( B , Gus ) = - n Tex ( de ) ... Moreover , formula ( 56 ) may clearly
be differentiated any number of times with respect to x , and still remain a valid ...
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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 |