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 2148
Since T is a spectral operator of class ( S ( T ) , * * ) , we have o ( T . ) Sõ and
consequently , is in p ( T . ) , which means that XI – T is a one - to - one map of E (
0 ) X into all of itself . Since 02 do ( T ) , we have E ( 0 ) 2 Eldo ( T ) ) = E ( S ) and
...
Since T is a spectral operator of class ( S ( T ) , * * ) , we have o ( T . ) Sõ and
consequently , is in p ( T . ) , which means that XI – T is a one - to - one map of E (
0 ) X into all of itself . Since 02 do ( T ) , we have E ( 0 ) 2 Eldo ( T ) ) = E ( S ) and
...
Page 2342
The matrix Ñik ( u ) of the remark following Regularity Hypothesis 1 is
consequently determined by the equations Ñ ex = 0 for 0 < k < v and v < is 2v , =
0 for v < k < 2v and isi sv , Ñ 1x = ( iwx ) " + otherwise , if k # 0 , k # v ; ÎN 10 = imi ,
isi şv ...
The matrix Ñik ( u ) of the remark following Regularity Hypothesis 1 is
consequently determined by the equations Ñ ex = 0 for 0 < k < v and v < is 2v , =
0 for v < k < 2v and isi sv , Ñ 1x = ( iwx ) " + otherwise , if k # 0 , k # v ; ÎN 10 = imi ,
isi şv ...
Page 2343
Consequently , if we use Lagrange ' s rule to expand this 2v X 2v determinant by
minors of order v , we find that the expansion contains only two non - vanishing
terms . Thus our 2v x 2v determinant may be expressed as P P2 + Q1Q2 , where
...
Consequently , if we use Lagrange ' s rule to expand this 2v X 2v determinant by
minors of order v , we find that the expansion contains only two non - vanishing
terms . Thus our 2v x 2v determinant may be expressed as P P2 + Q1Q2 , where
...
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Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1929 |
Copyright | |
28 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 countably additive 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 |