Suggestions for Further Work

Abstract

The study of Fourier series has a long and distinguished history in mathematics. Historically, Fourier series were introduced in order to solve the heat equation, and since then these series were frequently used in various applied problems. Much of modern real analysis including Lebesgue’s fundamental theory of integration had its origin in some deep convergence questions in Fourier series. In this book a basic analog of only relatively small part of an extensive theory of the Fourier series has been covered. The author truly believes that the most of the emerging theory of the q-Fourier series and practically all of their applications still remain “Terra Incognita” at the present stage of the investigation. The subject is rapidly changing and it is reasonable to expect that many more interesting results will be discovered in the future. In conclusion, I would like to outline several directions for further work.