ملخص
We apply universality limits to asymptotics of spacing of zeros {} fenced(xkn) of orthogonal polynomials, for weights with compact support and for exponential weights. A typical result isunder(lim, n → ∞) fenced(xkn - xk + 1, n) over(K, ̃)n fenced(xkn, xkn) = 1under minimal hypotheses on the weight, with over(K, ̃)n denoting a normalized reproducing kernel. Moreover, for exponential weights, we derive asymptotics for the differentiated kernels:Knfenced(r, s) fenced(x, x) = underover(∑, k = 0, n - 1) pkfenced(r) fenced(x) pkfenced(s) fenced(x) .
اللغة الأصلية | الإنجليزيّة |
---|---|
الصفحات (من إلى) | 69-95 |
عدد الصفحات | 27 |
دورية | Journal of Approximation Theory |
مستوى الصوت | 150 |
رقم الإصدار | 1 |
المعرِّفات الرقمية للأشياء | |
حالة النشر | نُشِر - يناير 2008 |
ملاحظة ببليوغرافية
Funding Information:Research supported by NSF Grant DMS0400446 and US-Israel BSF Grant 2004353. ∗Corresponding author. E-mail addresses: [email protected] (E. Levin), [email protected] (D.S. Lubinsky).