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 2343
Moreover , Q.Q2 is equal to the product etuiw , ) v + 1 ( iw , + 1 ) * v +1 ( iw2v - 1 ) v + 1 || ( iwa ) " ? ( iwa ) " i ( iw , ) " 1 etuiw . ) " + 2 " ( iw , ) ^ 2 V . " my +1 m1 m1 my 2 m2 m2 m2v my my e eiu ( iwo ) * 2v • ( iw2v - 1 ) ...
Moreover , Q.Q2 is equal to the product etuiw , ) v + 1 ( iw , + 1 ) * v +1 ( iw2v - 1 ) v + 1 || ( iwa ) " ? ( iwa ) " i ( iw , ) " 1 etuiw . ) " + 2 " ( iw , ) ^ 2 V . " my +1 m1 m1 my 2 m2 m2 m2v my my e eiu ( iwo ) * 2v • ( iw2v - 1 ) ...
Page 2365
Thus R ( ui ; T + P ) exists and equals C , proving by Definition 2.1 that T + P is discrete . Since by hypothesis D ( T - 1P ) 2 D ( T ' ) for 15 k , it follows that PD ( T ) = D ( T - 1 ) ...
Thus R ( ui ; T + P ) exists and equals C , proving by Definition 2.1 that T + P is discrete . Since by hypothesis D ( T - 1P ) 2 D ( T ' ) for 15 k , it follows that PD ( T ) = D ( T - 1 ) ...
Page 2389
Moreover , it follows similarly that at a point de eR for which pol > 82 but for which A ( 10 ) = 0 , R ( A ) has a pole of order at most equal to the order of the zero of A ( a ) at 1o . Finally , if 0 < ^ , < oo and A + ( 91 ) +0 ...
Moreover , it follows similarly that at a point de eR for which pol > 82 but for which A ( 10 ) = 0 , R ( A ) has a pole of order at most equal to the order of the zero of A ( a ) at 1o . Finally , if 0 < ^ , < oo and A + ( 91 ) +0 ...
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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 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 |