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1.
S. V. Khrushchev 《Journal of Approximation Theory》2002,116(2):268-342
The set
of all probability measures σ on the unit circle
splits into three disjoint subsets depending on properties of the derived set of {|n|2dσ}n0, denoted by Lim(σ). Here {n}n0 are orthogonal polynomials in L2(dσ). The first subset is the set of Rakhmanov measures, i.e., of σ
with {m}=Lim(σ), m being the normalized (m(
)=1) Lebesgue measure on
. The second subset Mar(
) consists of Markoff measures, i.e., of σ
with mLim(σ), and is in fact the subject of study for the present paper. A measure σ, belongs to Mar(
) iff there are >0 and l>0 such that sup{|an+j|:0jl}>, n=0,1,2,…,{an} is the Geronimus parameters (=reflectioncoefficients) of σ. We use this equivalence to describe the asymptotic behavior of the zeros of the corresponding orthogonal polynomials (see Theorem G). The third subset consists of σ
with {m}Lim(σ). We show that σ is ratio asymptotic iff either σ is a Rakhmanov measure or σ satisfies the López condition (which implies σMar(
)). Measures σ satisfying Lim(σ)={ν} (i.e., weakly asymptotic measures) are also classified. Either ν is the sum of equal point masses placed at the roots of zn=λ, λ
, n=1,2,…, or ν is the equilibrium measure (with respect to the logarithmic kernel) for the inverse image under an m-preserving endomorphism z→zn, n=1,2,…, of a closed arc J (including J=
) with removed open concentric arc J0 (including J0=). Next, weakly asymptotic measures are completely described in terms of their Geronimus parameters. Finally, we obtain explicit formulae for the parameters of the equilibrium measures ν and show that these measures satisfy {ν}=Lim(ν). 相似文献
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This article describes the neutron-diffraction system employed on the thermal column of the VVR-S reactor. The system can be used with liquid metals up to 1600 ° C and at angles from 0 ° to 100 °. 相似文献
4.
Rational compacts and exposed quadratic irrationalities 总被引:1,自引:1,他引:0
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Burdge G Alam SU Grudinin A Durkin M Ibsen M Khrushchev I White I 《Optics letters》1998,23(8):606-608
We present experimental results on ultrafast intensity modulation using the Raman effect and demonstrate 10-Gbit/s selective pulse erasure. The technique is both broadband and polarization insensitive and has a potential speed in excess of 500 Gbits/s. In addition to performing pulse erasure, this all-optical modulator can shape pulses as a precise, soft aperture scalpel and create short, dark pulses. 相似文献
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We study a construction of multiple stochastic integrals of nonrandom functions with respect to the product measures generated by stochastic processes admitting representations as multiple orthogonal random series. This construction is compared with some classical schemes of constructing stochastic integrals of such a kind. 相似文献