Inverse problems in Fourier analysis and summability theory
This is a survey paper of the problems indicated in the title. The fundamental results of \textit{L. Fejér} [J. Reine Angew. Math. 142, 165--188 (1913; JFM 44.0483.01)], \textit{F. Lukács} [ibid. 150, 107--112 (1920)], and their generalizations and extensions by the present author [Commun. Pure Appi. Math. 47, 653--681 (1994; Zbl 0802.42010)], by the reviewer [J. Fourier Anal. Appl. 7, 601--614 (2001; Zbl 1001.42008) and Proc. Am. Math. Soc. 131, 1243--1250 (2003; Zbl 1031.42002)], etc. have been developed into a coherent topic of Fourier Analysis. The present author not only provides an excellent account of these results, but also extends the investigations to a suitable class of summability kernels.
scientific article; zbMATH DE number 5015962