유계변동과 관련된 Waterman의 연구에 대하여

On the study of Waterman with respect to Bounded Variation

유계변동(bounded variation)과 관련된 Daniel Waterman의 30여 년간의 연구에 대하여 조사를 하였다.

Functions of bounded variation were discovered by Jordan in 1881 while working out the proof of Dirichlet concerning the convergence of Fourier series. Here, we investigate Waterman's study with respect to bounded variation and its application on a closed bounded interval. The value of his study is whether Dirichlet-Jordan theorem holds in which function classes or not and summability method is what modifies its Fourier coefficients to make resulting series converge to the associated function. We have a view that the directions of future research with respect to bounded variation are two things; one is to find the function spaces which are larger than HBV and smaller than ${\phi}BV$, and the other is to find a fields of applications.