The Size of the set of -Irregular Points of a measure
نویسندگان
چکیده
Let be a compactly suppported positive measure on the real line. A point x 2supp[ ] is said to be -regular, if, as n!1; sup deg(P ) n jP (x)j kPkL2(d ) !1=n ! 1: Otherwise it is a -irregular point. We show that for any such measure, the set of -irregular points in f 0 > 0g (with a suitable de nition of this set) has Hausdor¤mh measure 0, for h (t) = log 1 t , any > 1. Orthogonal Polynomials on the real line, regular measures, irregular points 1 Introduction1 Let be a positive measure on the real line, with compact support supp[ ], and in nitely many points in its support. is said to be regular in the sense of 1Research supported by NSF grant DMS1001182 and US-Israel BSF grant 2008399
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