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 2307
The last example above illustrates a problem which will be of great concern to us
in the remainder of this chapter : the problem of finding which formal differential
operators and sets of boundary conditions lead to spectral operators . As our ...
The last example above illustrates a problem which will be of great concern to us
in the remainder of this chapter : the problem of finding which formal differential
operators and sets of boundary conditions lead to spectral operators . As our ...
Page 2318
Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the
Assistance of William G. Bade and Robert G. ... Let T be the unbounded operator
in Hilbert space defined by the formal differential operator q = - ( d / dx ) 2 and the
...
Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the
Assistance of William G. Bade and Robert G. ... Let T be the unbounded operator
in Hilbert space defined by the formal differential operator q = - ( d / dx ) 2 and the
...
Page 2371
Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the
Assistance of William G. Bade and Robert G. Bartle Nelson Dunford, ... Let T be a
linear operator determined by the formal differential operator din In - 2 = = ( ) * + ...
Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the
Assistance of William G. Bade and Robert G. Bartle Nelson Dunford, ... Let T be a
linear operator determined by the formal differential operator din In - 2 = = ( ) * + ...
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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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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