Sergei Vladimirovich Konyagin turns 60

B. S. Kashin ; Yu. V. Malykhin ; V. Yu. Protasov ; K. S. Ryutin ; I. D. Shkredov

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Harmonic analysis, approximation theory, and number theory, Tome 303 (2018), pp. 7-16.

Bibliographie

[1] Hardy G. H., “On the summability of Fourier's series”, Proc. London Math. Soc. Ser. 2, 12 (1913), 365–372 | DOI | MR | Zbl

[2] Kolmogoroff A., “Une série de Fourier–Lebesgue divergente presque partout”, Fundam. math., 4 (1923), 324–328 | DOI | Zbl

[3] D. Menchoff, “Sur la représentation des fonctions mesurables par des séries trigonométriques”, Mat. Sb., 9:3 (1941), 667–692 | MR

[4] Gosselin R. P., “On the divergence of Fourier series”, Proc. Amer. Math. Soc., 9:2 (1958), 278–282 | DOI | MR | Zbl

[5] Chen Y.-M., “On Kolmogoroff's divergent Fourier series”, Arch. Math., 14 (1963), 116–119 | DOI | MR | Zbl

[6] Carleson L., “On convergence and growth of partial sums of Fourier series”, Acta math., 116 (1966), 135–157 | DOI | MR | Zbl

[7] S. V. Konyagin, “Approximation properties of arbitrary sets in Banach spaces”, Sov. Math., Dokl., 19 (1978), 309–312 | MR | Zbl

[8] S. V. Konyagin, “On approximation properties of closed sets in Banach spaces and the characterization of strongly convex spaces”, Sov. Math., Dokl., 21 (1980), 418–422 | MR | Zbl

[9] S. V. Konyagin, “Connectedness of sets in best approximation problems”, Sov. Math., Dokl., 24 (1981), 460–463 | MR | Zbl

[10] S. V. Konyagin, “On a problem of Littlewood”, Math. USSR, Izv., 18:2 (1981), 205–225 | DOI | MR | Zbl

[11] Körner T. W., “Everywhere divergent Fourier series”, Colloq. math., 45 (1981), 103–118 | DOI | MR | Zbl

[12] McGehee O. C., Pigno L., Smith B., “Hardy's inequality and the $L^1$ norm of exponential sums”, Ann. Math. Ser. 2, 113:3 (1981), 613–618 | DOI | MR | Zbl

[13] S. V. Konyagin, “Sets of points of nonemptiness and continuity of the metric projection”, Math. Notes, 33:5 (1983), 331–338 | DOI | MR | Zbl

[14] S. V. Konyagin, “On points of existence and nonuniqueness of best approximation elements”, Function Theory and Its Applications, Mosk. Gos. Univ., M., 1986, 38–43 (in Russian)

[15] S. V. Konyagin, I. G. Tsar'kov, “Efimov–Stechkin spaces”, Moscow Univ. Math. Bull., 41:5 (1986), 20–28 | MR | Zbl

[16] A. L. Vol'berg, S. V. Konyagin, “On measures with the doubling condition”, Math. USSR, Izv., 30:3 (1988), 629–638 | DOI | MR | Zbl | Zbl

[17] S. V. Konyagin, “Divergence in measure of multiple Fourier series”, Math. Notes, 44:2 (1988), 589–592 | DOI | MR | MR | Zbl

[18] S. V. Konyagin, “On continuous operators of generalized rational approximation”, Mat. Zametki, 44:3 (1988), 404 | MR | Zbl

[19] S. V. Konyagin, “Limits of indeterminacy of trigonometric series”, Math. Notes, 44:6 (1988), 910–920 | DOI | MR | MR | Zbl

[20] S. V. Konyagin, “On rearrangements of functions and divergence of Fourier series over cubes”, Proc. Steklov Inst. Math., 189 (1990), 111–125 | MR | Zbl | Zbl

[21] S. V. Konyagin, “On divergence of a subsequence of the partial sums of multiple trigonometric Fourier series”, Proc. Steklov Inst. Math., 190 (1992), 107–121 | MR | Zbl

[22] S. V. Konyagin, “On almost everywhere divergence of sequences of rectangular partial sums of double trigonometric series”, Reports of Extended Sessions of the Seminar at the Vekua Institute of Applied Mathematics, 5, no. 2, Tbil. Gos. Univ., Tbilisi, 1990, 71–74 (in Russian)

[23] S. V. Konyagin, “On divergence of Fourier series with respect to a rearranged trigonometric system”, Mat. Zametki, 47:6 (1990), 143–145 | MR | Zbl

[24] S. V. Konyagin, “A problem of Littlewood”, Math. Notes, 49:2 (1991), 217–218 | DOI | MR | MR | Zbl

[25] S. V. Konyagin, “Convergence of subsequences of partial cubic sums of Fourier series in mean and almost everywhere”, Math. Notes, 52:3 (1992), 918–930 | DOI | MR | Zbl

[26] Konyagin S. V., “On the level sets of Lipschitz functions”, Tatra Mt. Math. Publ., 2 (1993), 51–59 | MR | Zbl

[27] S. V. Konyagin, “Minimum of the absolute value of random trigonometric polynomials with coefficients $\pm 1$”, Math. Notes, 56:3 (1994), 931–947 | DOI | MR | Zbl

[28] Konyagin S. V., “On points of existence of elements of best approximation by sets in reflexive spaces”, East J. Approx., 1:1 (1995), 141–142 | MR | Zbl

[29] Konyagin S. V., “On divergence of trigonometric Fourier series over cubes”, Acta sci. math., 61 (1995), 305–329 | MR | Zbl

[30] Antonov N. Yu., “Convergence of Fourier series”, East J. Approx., 2:2 (1996), 187–196 | MR | Zbl

[31] A. S. Belov, S. V. Konyagin, “An estimate of the free term of a non-negative trigonometric polynomial with integer coefficients”, Izv. Math., 60:6 (1996), 1123–1182 | DOI | DOI | MR | Zbl

[32] V. Yu. Protasov, “The joint spectral radius and invariant sets of linear operators”, Fundam. Prikl. Mat., 2:1 (1996), 205–231 | MR | Zbl

[33] Konyagin S. V., “Estimates of maxima of sine sums”, East J. Approx., 3:1 (1997), 63–70 | MR | Zbl

[34] Konyagin S., “On a question of Pichorides”, C. r. Acad. sci. Paris. Sér. 1, 324:4 (1997), 385–388 | DOI | MR | Zbl

[35] S. V. Konyagin, “On approximative properties of arbitrary closed sets in Banach spaces”, Fundam. Prikl. Mat., 3:4 (1997), 979–989 | MR | Zbl

[36] Konyagin S. V., Shparlinski I. E., Character sums with exponential functions and their applications, Cambridge Tracts Math., 136, Cambridge Univ. Press, Cambridge, 1999 | MR | Zbl

[37] Konyagin S. V., Schlag W., “Lower bounds for the absolute value of random polynomials on a neighborhood of the unit circle”, Trans. Amer. Math. Soc., 351:12 (1999), 4963–4980 | DOI | MR | Zbl

[38] S. V. Konyagin, “On everywhere divergence of trigonometric Fourier series”, Sb. Math., 191:1 (2000), 97–120 | DOI | DOI | MR | Zbl

[39] Konyagin S. V., “Rearrangements of trigonometric series and trigonometric polynomials”, Real Anal. Exch., 29:1 (2003–2004), 323–334 | DOI | MR

[40] Konyagin S. V., Temlyakov V. N., “Convergence of greedy approximation. I: General systems”, Stud. math., 159:1 (2003), 143–160 | DOI | MR | Zbl

[41] Konyagin S. V., Temlyakov V. N., “Convergence of greedy approximation. II: The trigonometric system”, Stud. math., 159:2 (2003), 161–184 | DOI | MR | Zbl

[42] N. Yu. Antonov, “Almost everywhere convergence over cubes of multiple trigonometric Fourier series”, Izv. Math., 68:2 (2004), 223–241 | DOI | DOI | MR | Zbl

[43] S. V. Konyagin, “Divergence everywhere of subsequences of partial sums of trigonometric Fourier series”, Proc. Steklov Inst. Math., 2005, Suppl. 2, 167–175 | MR | Zbl

[44] Bourgain J., Glibichuk A. A., Konyagin S. V., “Estimates for the number of sums and products and for exponential sums in fields of prime order”, J. London Math. Soc. Ser. 2, 73:2 (2006), 380–398 | DOI | MR | Zbl

[45] S. V. Konyagin, “On uniformly convergent rearrangements of trigonometric Fourier series”, J. Math. Sci., 155:1 (2008), 81–88 | DOI | MR | Zbl

[46] Konyagin S., “Good distribution of values of sparse polynomials modulo a prime”, Analytic number theory, Essays in honor of Klaus Roth, Cambridge Univ. Press, Cambridge, 2009, 289–296 | MR | Zbl

[47] S. V. Konyagin, “Almost everywhere divergence of lacunary subsequences of partial sums of Fourier series”, Proc. Steklov Inst. Math., 273, Suppl. 1 (2011), 99–106 | DOI | MR | Zbl

[48] Bourgain J., Dilworth S., Ford K., Konyagin S., Kutzarova D., “Explicit constructions of RIP matrices and related problems”, Duke Math. J., 159:1 (2011), 145–185 | DOI | MR | Zbl

[49] Bourgain J., Konyagin S. V., Shparlinski I. E., “Distribution of elements of cosets of small subgroups and applications”, Int. Math. Res. Not., 2012:9 (2012), 1968–2009 | MR | Zbl

[50] Konyagin S. V., Shparlinski I. E., “On the consecutive powers of a primitive root: gaps and exponential sums”, Mathematika, 58:1 (2012), 11–20 | DOI | MR | Zbl

[51] Lie V., “On the pointwise convergence of the sequence of partial Fourier sums along lacunary subsequences”, J. Funct. Anal., 263:11 (2012), 3391–3411 | DOI | MR | Zbl

[52] Konyagin S. V., Rudnev M., “On new sum–product-type estimates”, SIAM J. Discrete Math., 27:2 (2013), 973–990 | DOI | MR | Zbl

[53] Di Plinio F., “Lacunary Fourier and Walsh–Fourier series near $L^1$”, Collect. math., 65:2 (2014), 219–232 | DOI | MR | Zbl

[54] Konyagin S., “$h$-Fold sums from a set with few products”, Moscow J. Comb. Number Theory, 4:3 (2014), 14–20 | MR | Zbl

[55] S. V. Konyagin, “Deviation of elements of a Banach space from a system of subspaces”, Proc. Steklov Inst. Math., 284 (2014), 204–207 | DOI | MR | Zbl

[56] Lie V., “Pointwise convergence of Fourier series. I: On a conjecture of Konyagin”, J. Eur. Math. Soc., 19:6 (2017), 1655–1728 | DOI | MR | Zbl

[57] Bourgain J., Konyagin S. V., Shparlinski I. E., “Character sums and deterministic polynomial root finding in finite fields”, Math. Comput., 84:296 (2015), 2969–2977 | DOI | MR | Zbl

[58] S. V. Konyagin, I. D. Shkredov, “On sum sets of sets having small product set”, Proc. Steklov Inst. Math., 290 (2015), 288–299 | DOI | MR | Zbl

[59] S. V. Konyagin, I. D. Shkredov, “New results on sums and products in $\mathbb R$”, Proc. Steklov Inst. Math., 294 (2016), 78–88 | DOI | MR | Zbl

[60] Maynard J., “Large gaps between primes”, Ann. Math. Ser. 2, 183:3 (2016), 915–933 | DOI | MR | Zbl

[61] Ford K., Green B., Konyagin S., Tao T., “Large gaps between consecutive prime numbers”, Ann. Math. Ser. 2, 183:3 (2016), 935–974 | DOI | MR | Zbl

[62] Ford K., Green B., Konyagin S., Maynard J., Tao T., “Long gaps between primes”, J. Amer. Math. Soc., 31:1 (2018), 65–105 | DOI | MR | Zbl

[63] Borodin P. A., Konyagin S. V., “Convergence to zero of exponential sums with positive integer coefficients and approximation by sums of shifts of a single function on the line”, Anal. math., 44:2 (2018), 163–183 | DOI | MR | Zbl