Linear Operators: Spectral operators |
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Page 1913
... properties of spectral operators that distinguish them from other operators . These properties assume a variety of forms not immediately apparent from the definition of a spectral operator . For example , the spectral relations ...
... properties of spectral operators that distinguish them from other operators . These properties assume a variety of forms not immediately apparent from the definition of a spectral operator . For example , the spectral relations ...
Page 2211
... properties ( vi ) , it follows from ( iv ) that f , g , so that the properties ( vi ) characterize ƒ , · It will next be observed that ( vii ) - OFz = σ ( F ) σ2 , FEB . To prove this , note first that ( E , F ) Fx = FE , x = Fx , so ...
... properties ( vi ) , it follows from ( iv ) that f , g , so that the properties ( vi ) characterize ƒ , · It will next be observed that ( vii ) - OFz = σ ( F ) σ2 , FEB . To prove this , note first that ( E , F ) Fx = FE , x = Fx , so ...
Page 2588
... properties of , XVII.3.3 ( 2196 ) , XVII- .3.4 ( 2197 ) , XVII.3.5 ( 2198 ) , XVII.3.6 ( 2199 ) , XVII.3.7-8 ( 2201 ) , XVII.3.9 ( 2202 ) , XVII.3.10 ( 2204 ) , XVII.3.11 ( 2204 ) , XVII.3.13 ( 2207 ) , XVII.3.14 ( 2208 ) , XVII- .3.15 ...
... properties of , XVII.3.3 ( 2196 ) , XVII- .3.4 ( 2197 ) , XVII.3.5 ( 2198 ) , XVII.3.6 ( 2199 ) , XVII.3.7-8 ( 2201 ) , XVII.3.9 ( 2202 ) , XVII.3.10 ( 2204 ) , XVII.3.11 ( 2204 ) , XVII.3.13 ( 2207 ) , XVII.3.14 ( 2208 ) , XVII- .3.15 ...
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