Properties of sequence of linear functionals on BV with applications

L. E. Persson Persson; V. Tsagareishvili; G. Tutberidze

L. E. Persson Persson UiT-The Arctic University of Norway, P.O. Box 385, N-8505, Narvik, Norway and Department of Mathematics and Computer Science, Karlstad University, 65188 Karlstad, Sweden
V. Tsagareishvili Ivane Javakhishvili Tbilisi State University, Chavchavadze str. 1, Tbilisi 0128, Georgia.
G. Tutberidze School of science and technology, 77a Merab Kostava St, Tbilisi 0128, Georgia.

Abstract

This paper is devoted to investigating a sequence of some linear functionals in the space $BV$ of finite variation functions. We prove that under certain conditions this sequence is bounded. We also prove that this result is sharp. In particular, the obtained results can be used to study convergence of some general Fourier series. Moreover, the obtained conditions seem to be new and useful also for classical orthonormal systems.