ON A UNIQUENESS THEOREM FOR THE FRANKLIN SYSTEM K Navasard
In this paper we prove that there exist a nontrivial Franklin series and asequenceMnsuch that the partial sumsSMn(x)of that series converge to 0almost everywhere andλ·mes{x: supn|SMn(x)|>λ}→0 asλ→+∞.Thisshows that the boundedness assumption of the ratioMn+1Mn, used for the proofsof uniqueness theorems in earlier papers, can not be omitted
DOI: 10.46991/PYSU:A/2018.52.2.093 Physical and Mathematical Sciences, 52(2 (246) 93-100
