Gridnev, Maxim L. Divergence of the Fourier series of continuous functions with a restriction on the fractality of their graphs. (English) Zbl 1448.42010 Ural Math. J. 3, No. 2, 46-50 (2017). Summary: We consider certain classes of functions with a restriction on the fractality of their graphs. Modifying Lebesgue’s example, we construct continuous functions from these classes whose Fourier series diverge at one point, i.e. the Fourier series of continuous functions from this classes do not converge everywhere. MSC: 42A20 Convergence and absolute convergence of Fourier and trigonometric series Keywords:trigonometric Fourier series; fractality; divergence at one point; continuous functions PDF BibTeX XML Cite \textit{M. L. Gridnev}, Ural Math. J. 3, No. 2, 46--50 (2017; Zbl 1448.42010) Full Text: DOI MNR OpenURL References: [1] Bari N.K., Trigonometric series, Fizmatgiz, Moscow, 1961, 936 pp. (in Russian) [2] Salem R., Essais sur les séries trigonométriques., v. 862, Actual. Sci. et Industr., 1940 · JFM 66.0280.01 [3] Waterman D., “On converges of Fourier series of functions of generalized bounded variation”, Studia Mathematica, 44 (1972), 107-117 · Zbl 0207.06901 [4] Gridnev M. L., “About classes of functions with a restriction on the fractality of their graphs”, Proceedings of the 48th Intern. Youth School-Conf.: Modern Problems in Mathematics and its Applications (Ekaterinburg, February 5-11, 2017), CEUR-WS Proceedings, 1894, 2017, 167-3 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.