Linear Operators: Spectral operators |
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Page 2025
... gives Σkj ( 8 ) ) √x1 ( 8 ) | n ( 40 ) 12 1 = | 4 ( s ) | ≤ M ( λ — w ) r n = 1 , 2 , .... - Since ( ( $ ) ) > w we may fix A so large that | — ( $ ) | < λ — w and thus the fraction appearing in ( 40 ) approaches zero as no . Q.E.D. ...
... gives Σkj ( 8 ) ) √x1 ( 8 ) | n ( 40 ) 12 1 = | 4 ( s ) | ≤ M ( λ — w ) r n = 1 , 2 , .... - Since ( ( $ ) ) > w we may fix A so large that | — ( $ ) | < λ — w and thus the fraction appearing in ( 40 ) approaches zero as no . Q.E.D. ...
Page 2031
... gives ( FT ̧ ) ( q ) = √ ( Fq ) ( s ) 4 ( s ) ds = { _q ( 8 ) ( F4 ) ( s ) ds = Tr « ( 4 ) , RN RN - ΦΕΦ in Now is dense in H = L2 ( R ) and thus there is for an arbitrary 5 a sequence { n } with n → in 5. Since F ( XI.1 ) and F is ...
... gives ( FT ̧ ) ( q ) = √ ( Fq ) ( s ) 4 ( s ) ds = { _q ( 8 ) ( F4 ) ( s ) ds = Tr « ( 4 ) , RN RN - ΦΕΦ in Now is dense in H = L2 ( R ) and thus there is for an arbitrary 5 a sequence { n } with n → in 5. Since F ( XI.1 ) and F is ...
Page 2065
... gives more by asserting that the inverse a - 1 is in A1 . The basic notions underlying the proof of Wiener's theorem as it will be presented here are those to be found in I. M. Gelfand's theory of com- mutative normed rings , or B ...
... gives more by asserting that the inverse a - 1 is in A1 . The basic notions underlying the proof of Wiener's theorem as it will be presented here are those to be found in I. M. Gelfand's theory of com- mutative normed rings , or B ...
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