Linear Operators: Spectral operators |
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Page 2011
... defined almost everywhere on but not necessarily bounded . For every set σ in Σ and every such matrix  ( s ) we ... defined operator . In general , however ,  , need not be bounded but it is always a closed and densely defined operator ...
... defined almost everywhere on but not necessarily bounded . For every set σ in Σ and every such matrix  ( s ) we ... defined operator . In general , however ,  , need not be bounded but it is always a closed and densely defined operator ...
Page 2018
... defined ( see Section VII.9 ) as the set of all complex numbers À for which ( I — A ) -1 exists as a bounded everywhere defined operator . The spectrum o ( A ) of A is defined to be the complement p ( A ) . It is clear from the equation ...
... defined ( see Section VII.9 ) as the set of all complex numbers À for which ( I — A ) -1 exists as a bounded everywhere defined operator . The spectrum o ( A ) of A is defined to be the complement p ( A ) . It is clear from the equation ...
Page 2284
... defined and continuous , and the map AWT is a densely defined closed map of E , X into H , with densely defined inverse . We suppose the norm of [ h1 , h ] in 5 , is defined to be n = 1 n n 1/2 so that H is a Hilbert space . It is ...
... defined and continuous , and the map AWT is a densely defined closed map of E , X into H , with densely defined inverse . We suppose the norm of [ h1 , h ] in 5 , is defined to be n = 1 n n 1/2 so that H is a Hilbert space . It is ...
Contents
SPECTRAL OPERATORS | 1924 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
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A₁ algebra Amer analytic applications arbitrary B-space Banach Banach space Boolean algebra Borel sets boundary bounded Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding defined Definition denote dense determined differential operator Doklady Akad elements equation equivalent established example exists extension finite follows formula function given gives H₁ Hence Hilbert space hypothesis identity integral invariant inverse Lemma limit linear operators Math multiplicity Nauk SSSR norm normal perturbation plane positive preceding present problem Proc projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero