On the scientific work of Kunyang Wang

Abstract

This paper surveys some of the scientific work on positive polynomial sums, Fourier analysis and spherical approximation on the sphere that Kunyang Wang did in the past 20 years. Int. J. Wavelets Multiresolut Inf. Process. 2014.12. Downloaded from www.worldscientific.com by FLINDERS UNIVERSITY LIBRARY on 02/05/15. For personal use only. 1461003-2 Int. J. Wavelets Multiresolut Inf. Process. 2014.12. Downloaded from www.worldscientific.com by FLINDERS UNIVERSITY LIBRARY on 02/05/15. For personal use only. On the scientific work of Kunyang Wang Problem 1 is closely related to a second problem raised by Szegö in Ref. 36: Problem 2. Characterize all values of α such that z 0 t −α J α (t)dt > 0 (1.3) holds for all z > 0. Since lim n→∞ C ν n cos z n C ν n (1)uniformly in every fixed disk |z| ≤ R, it follows that for all z > 0Thus, the result of Brown, Koumandos and Wang 17 implies thatProblem 2 was solved by Szegö, 36 who showed that z 0 t −α J α (t)dt > 0 for all z > 0 if α > α and this inequality fails for some z > 0 for each α < α .