Linear Operators: Spectral operators |
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Page 1986
... establish the inversion formula ( 5 ) . Once this is done , it will follow that F is one - to - one on and that q ( s ) = ( F2q ) ( - s ) , which proves that FØ Ø and thus that the ... established by 1986 XV.11.1 XV . SPECTRAL OPERATORS.
... establish the inversion formula ( 5 ) . Once this is done , it will follow that F is one - to - one on and that q ( s ) = ( F2q ) ( - s ) , which proves that FØ Ø and thus that the ... established by 1986 XV.11.1 XV . SPECTRAL OPERATORS.
Page 2212
... establish the equation ( viii ) fF1 = f1 Xo ( F ) , Fe B. To prove this , let g = fr Xo ( F ) so that , using ( vii ) , we ... established . Hence we may and shall assume , in the proof of ( ix ) , that = Since A ( x − y ) = Ax — Ay it ...
... establish the equation ( viii ) fF1 = f1 Xo ( F ) , Fe B. To prove this , let g = fr Xo ( F ) so that , using ( vii ) , we ... established . Hence we may and shall assume , in the proof of ( ix ) , that = Since A ( x − y ) = Ax — Ay it ...
Page 2234
... established for bounded Borel sets with closures contained in U , n f ( TE ( e ) X ) x = lim f ( T | F ( en ) E ( e ) X ) F ( en ) x = 1200 lim ƒ ( T | E ( een ) X ) E ( en ) x 2200 lim f ( T ) E ( en ) x . Since E ( e ) xx , and since ...
... established for bounded Borel sets with closures contained in U , n f ( TE ( e ) X ) x = lim f ( T | F ( en ) E ( e ) X ) F ( en ) x = 1200 lim ƒ ( T | E ( een ) X ) E ( en ) x 2200 lim f ( T ) E ( en ) x . Since E ( e ) xx , and since ...
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