Determination of a jump by Fourier and Fourier-Chebyshev series

Abstract

By observing the equivalence of assertions on determining the jump of a function by its differentiated or integrated Fourier series, we generalize a previous result of Kvernadze, Hagstrom and Shapiro to the whole class of functions of harmonic bounded variation and without finiteness assumption on the number of discontinuities. Two results on determination of jump discontinuities by means of the tails of integrated Fourier-Chebyshev series are derived.

arXiv comment15 pages; New Proposition 3.1 and Corollary 3.2. are introduced. The previous Theorem 3.2 is replaced by Theorem 3.4 related to the Chebyshev system, not the generalized Jacobi system. This is reflected in the Abstract and a more accurate title of the paper