In the present paper we consider sequences of rational functions with a bounded number or free poles con- verging uniformly with a maximum geometric rate to a holomorphic function on a regular set,and we examine the l...In the present paper we consider sequences of rational functions with a bounded number or free poles con- verging uniformly with a maximum geometric rate to a holomorphic function on a regular set,and we examine the limiting distribution of the Zeros and its relations with the phenomenon of overconvergence.Our results further extend the well known classical theory of overconvergence and the zeros of sections of Taylor series.展开更多
In this paper. a quantitative estimate for Hermite interpolant to function ψ(z)=(z^m-β~m)~l on the ze- ros of (z^n-α~n)~r is obtained Using this estimate. a rather wide exiension of the theorem of Walsh is proved a...In this paper. a quantitative estimate for Hermite interpolant to function ψ(z)=(z^m-β~m)~l on the ze- ros of (z^n-α~n)~r is obtained Using this estimate. a rather wide exiension of the theorem of Walsh is proved and five special cases of it are given.展开更多
In the present article, we deal with the so-called overconvergence phenomenon in C of a slightly modified Post-Widder operator of real variable, that is with the extension of its approximation properties from the real...In the present article, we deal with the so-called overconvergence phenomenon in C of a slightly modified Post-Widder operator of real variable, that is with the extension of its approximation properties from the real axis in the complex plane.In this sense, error estimates in approximation and a quantitative Voronovskaya-type asymptotic formula are established.展开更多
We formulate a local analogue of the ghost conjecture of Bergdall and Pollack,which essentially relies purely on the representation theory of GL_(2)(Q_(p)).We further study the combinatorial properties of the ghost se...We formulate a local analogue of the ghost conjecture of Bergdall and Pollack,which essentially relies purely on the representation theory of GL_(2)(Q_(p)).We further study the combinatorial properties of the ghost series as well as its Newton polygon,in particular,giving a characterization of the vertices of the Newton polygon and proving an integrality result of the slopes.In a forthcoming sequel,we will prove this local ghost conjecture under some mild hypothesis and give arithmetic applications.展开更多
文摘In the present paper we consider sequences of rational functions with a bounded number or free poles con- verging uniformly with a maximum geometric rate to a holomorphic function on a regular set,and we examine the limiting distribution of the Zeros and its relations with the phenomenon of overconvergence.Our results further extend the well known classical theory of overconvergence and the zeros of sections of Taylor series.
基金The Project is supported by National Natural Science Foundation of China.
文摘In this paper. a quantitative estimate for Hermite interpolant to function ψ(z)=(z^m-β~m)~l on the ze- ros of (z^n-α~n)~r is obtained Using this estimate. a rather wide exiension of the theorem of Walsh is proved and five special cases of it are given.
文摘In the present article, we deal with the so-called overconvergence phenomenon in C of a slightly modified Post-Widder operator of real variable, that is with the extension of its approximation properties from the real axis in the complex plane.In this sense, error estimates in approximation and a quantitative Voronovskaya-type asymptotic formula are established.
基金R.Liu is partially supported by the National Natural Science Foundation of China under Agreement No.NSFC-11725101 and the Tencent FoundationN.Truong is partially supported by L.Xiao’s NSF under Grant DMS-1752703+3 种基金L.Xiao is partially supported by Simons Collaboration under Grant#278433NSF under Grant DMS-1502147 and DMS-1752703the Chinese NSF grant NSFC-12071004,Recruitment Program of Global Experts of China,and a grant from the Chinese Ministry of EducationB.Zhao is partially supported by AMS-Simons Travel Grant.
文摘We formulate a local analogue of the ghost conjecture of Bergdall and Pollack,which essentially relies purely on the representation theory of GL_(2)(Q_(p)).We further study the combinatorial properties of the ghost series as well as its Newton polygon,in particular,giving a characterization of the vertices of the Newton polygon and proving an integrality result of the slopes.In a forthcoming sequel,we will prove this local ghost conjecture under some mild hypothesis and give arithmetic applications.
