Trigonometric Fourier series of continuous functions diverging on a given set
Sbornik. Mathematics, Tome 24 (1974) no. 1, pp. 79-102 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this work divergent trigonometric Fourier series of continuous functions are investigated. Certain types of sets are determined which are sets of divergence, unbounded divergence and bounded divergence for Fourier series of continuous functions. From these results it follows that there exist sets of bounded divergence having Hausdorff dimension 1 and also sets having positive $\alpha$-capacity. Bibliography: 19 titles.
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V. V. Buzdalin. Trigonometric Fourier series of continuous functions diverging on a given set. Sbornik. Mathematics, Tome 24 (1974) no. 1, pp. 79-102. http://geodesic.mathdoc.fr/item/SM_1974_24_1_a4/

[1] N. K. Bari, Trigonometricheskie ryady, Fizmatgiz, Moskva, 1961 | MR

[2] P. Du Bois-Reymond, “Untersuchungen über die Convergenz und Divergenz der Fourierschen Darstellungsformen”, Abh. Akad. Wiss. München, X (1876), 1–103

[3] N. Lusin, “Über eine Potenzreihe”, Rend. circ. Mat. Palermo, 32 (1911), 386–390 | DOI | Zbl

[4] H. Steinhaus, “Sur une serie trigonometrique divergente”, C. r. de la Soc. Sci. de Varsovie, V:3 (1912), 223–227

[5] H. Steinhaus, “Sur un problem de N. N. Lusin et Sierpinski”, Bull. Acad. Sci Cracovie, 1913, 435–450 | Zbl

[6] A. Rajchman, “Sur le principe de localisation de Riemann”, C. r. de la Soc. Sci. de Varsovie, 11 (1918), 115–122

[7] A. Kolmogoroff, “Une serie de Fourier-Lebesgue divergente partout”, C. r. Acad. Sci., Paris, 183 (1926), 1327–1328 | Zbl

[8] S. B. Stechkin, “O skhodimosti i raskhodimosti trigonometricheskikh ryadov”, Uspekhi matem. nauk, VI:2 (42) (1951), 148–149

[9] S. B. Stechkin, “O trigonometricheskikh ryadakh, raskhodyaschikhsya v kazhdoi tochke”, Izv. AN SSSR, seriya matem., 21 (1957), 711–728 | Zbl

[10] K. Zeller, “Über Konvergenzmengen von Fourierreihen”, Arch. Math., 6:4 (1955), 335–340 | DOI | MR | Zbl

[11] P. L. Ulyanov, “O raskhodimosti ryadov Fure”, Uspekhi matem. nauk, XII:3 (75) (1957), 75–132 | MR

[12] J. Sladkowska, “Sur les ensembles des points de divergence des series de Fourier des fonctions continues”, C. r. Acad. Sci., Paris, ser. A, 250 (1960), 258–259 | MR | Zbl

[13] J. Sladkowska, “Sur les ensembles des points de divergence des series de Fourier des fonctions continues”, Fundam. math., XLIX (1961), 271–294 | MR

[14] L. V. Taikov, “O raskhodimosti ryadov Fure po perestavlennoi trigonometricheskoi sisteme”, Uspekhi matem. nauk, XVIII:5 (113) (1963), 191–198 | MR

[15] J-P. Kahane, Y. Katznelson, “Sur les ensembles de divergence des series trigonometriques”, Studia math., XXVI (1966), 305–306 | MR

[16] V. V. Buzdalin, “O neogranichenno raskhodyaschikhsya trigonometricheskikh ryadakh Fure ot nepreryvnykh funktsii”, Matem. zametki, 7:1 (1970), 7–18 | MR

[17] L. V. Taikov, “O raskhodimosti vsyudu perestavlennykh ryadov Fure nepreryvnykh funktsii”, Matem. zametki, 9:4 (1971), 459–465 | MR | Zbl

[18] T. W. Körner, “Sets of divergence for Fourier series”, Bull. London Math. Soc., 3:2 (1971), 152–154 | DOI | MR | Zbl

[19] A. Grennberg, Sets of divergence of Fourier series, Report No 1, University of Umea, Sweden, Department of Mathematics, 1972, 1–20 | MR