ملخص
Let μ be a compactly suppported positive measure on the real line. A point x∈supp [μ] is said to be μ-regular, if, as n → ∞, Otherwise it is a μ-irregular point. We show that for any such measure, the set of μ-irregular points in {μ′>0} (with a suitable definition of this set) has Hausdorff mhβ measure 0, for hβ(t) = (log 1/t)-β, any β>1.
| اللغة الأصلية | الإنجليزيّة |
|---|---|
| الصفحات (من إلى) | 242-250 |
| عدد الصفحات | 9 |
| دورية | Acta Mathematica Hungarica |
| مستوى الصوت | 133 |
| رقم الإصدار | 3 |
| المعرِّفات الرقمية للأشياء | |
| حالة النشر | نُشِر - نوفمبر 2011 |
ملاحظة ببليوغرافية
Funding Information:∗Corresponding author. †Research supported by NSF grant DMS1001182 and US-Israel BSF grant 2008399. Key words and phrases: orthogonal polynomial on the real line, regular measure, irregular point. 2000 Mathematics Subject Classification: 42C05, 42C99.