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 1926
... a a NEO ( T ) which is not valid for an arbitrary T. To see more clearly the difference between the calculi given by these two formulas , let us rewrite them by introducing the nilpotent N and the resolution of the identity E ...
... a a NEO ( T ) which is not valid for an arbitrary T. To see more clearly the difference between the calculi given by these two formulas , let us rewrite them by introducing the nilpotent N and the resolution of the identity E ...
Page 2031
... an arbitrary 4 in H a sequence { n } co with yn → in H. Since FQ = 0 ( XI.1 ) and F is continuous on H , the inequality ( ii ) shows that FTvn → FT ) . On the other . hand , the preceding equation shows that FT - n = Trun which by ...
... an arbitrary 4 in H a sequence { n } co with yn → in H. Since FQ = 0 ( XI.1 ) and F is continuous on H , the inequality ( ii ) shows that FTvn → FT ) . On the other . hand , the preceding equation shows that FT - n = Trun which by ...
Page 2314
Let ko , k , be arbitrary constants and let T be the unbounded operator in L , ( 0 , 1 ) defined by the formal differential operator t = -d / dt ) 2 and the boundary conditions f ( 0 ) – ko f ' ( 0 ) = 0 , f ( 1 ) – kif ' ( 1 ) = 0 .
Let ko , k , be arbitrary constants and let T be the unbounded operator in L , ( 0 , 1 ) defined by the formal differential operator t = -d / dt ) 2 and the boundary conditions f ( 0 ) – ko f ' ( 0 ) = 0 , f ( 1 ) – kif ' ( 1 ) = 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 |