George Lorentz and inequalities in approximation
Algebra i analiz, Tome 21 (2009) no. 3, pp. 1-57.

Voir la notice de l'article provenant de la source Math-Net.Ru

George Lorentz influenced the author's research on inequalities in approximation in many ways. This is the connecting thread of this survey paper. The themes of the survey are listed at the very beginning of the paper.
@article{AA_2009_21_3_a0,
     author = {T. Erd\'elyi},
     title = {George {Lorentz} and inequalities in approximation},
     journal = {Algebra i analiz},
     pages = {1--57},
     publisher = {mathdoc},
     volume = {21},
     number = {3},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AA_2009_21_3_a0/}
}
TY  - JOUR
AU  - T. Erdélyi
TI  - George Lorentz and inequalities in approximation
JO  - Algebra i analiz
PY  - 2009
SP  - 1
EP  - 57
VL  - 21
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AA_2009_21_3_a0/
LA  - en
ID  - AA_2009_21_3_a0
ER  - 
%0 Journal Article
%A T. Erdélyi
%T George Lorentz and inequalities in approximation
%J Algebra i analiz
%D 2009
%P 1-57
%V 21
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AA_2009_21_3_a0/
%G en
%F AA_2009_21_3_a0
T. Erdélyi. George Lorentz and inequalities in approximation. Algebra i analiz, Tome 21 (2009) no. 3, pp. 1-57. http://geodesic.mathdoc.fr/item/AA_2009_21_3_a0/

[1] Amoroso F., “Sur le diamètre transfini entier d'un intervalle réel”, Ann. Inst. Fourier (Grenoble), 40 (1990), 885–911, (1991) | MR | Zbl

[2] Arestov V. V., “Ob integralnykh neravenstvakh dlya trigonometricheskikh polinomov i ikh proizvodnykh”, Izv. AN SSSR. Ser. mat., 45:1 (1981), 3–22 | MR | Zbl

[3] Bak J., Newman D. J., “Rational combinations of $x^{\lambda_k}$, $\lambda_k\geq0$, are always dense in $C[0,1]$”, J. Approx. Theory, 23 (1978), 155–157 | DOI | MR | Zbl

[4] Bastero J., “$\ell_q$-subspaces of stable $p$-Banach spaces, $0

\le 1$”, Arch. Math. (Basel), 40 (1983), 538–544 | MR | Zbl

[5] Beck J., “Flat polynomials on the unit circle – note on a problem of Littlewood”, Bull. London Math. Soc., 23 (1991), 269–277 | DOI | MR | Zbl

[6] Benko D., Erdélyi T., “Markov inequality for polynomials of degree $n$ with $m$ distinct zeros”, J. Approx. Theory, 122 (2003), 241–248 | MR | Zbl

[7] Benko D., Erdélyi T., Szabados J., “The full Markov–Newman inequality for Müntz polynomials on positive intervals”, Proc. Amer. Math. Soc., 131 (2003), 2385–2391, (electronic) | DOI | MR | Zbl

[8] Bernshtein C. H., “O predstavlenii polozhitelnykh mnogochlenov”, Konstruktivnaya teoriya funktsii, Sobranie sochinenii. T. 1, AN SSSR, M., 1952, 251–252

[9] Beaucoup F., Borwein P., Boyd D., Pinner C., “Multiple roots of $[-1,1]$ power series”, J. London Math. Soc. (2), 57:1 (1998), 135–147 | DOI | MR | Zbl

[10] Bloch A., Pólya G., “On the roots of certain algebraic equations”, Proc. London Math. Soc. (2), 33 (1932), 102–114 | DOI

[11] Bombieri E., Vaaler J., “Polynomials with low height and prescribed vanishing”, Analytic Number Theory and Diophantine Problems (Stillwater, OK, 1984), Progr. Math., 70, Birkhäuser Boston, Boston, MA, 1987, 53–73 | MR

[12] Borwein P., “Markov's inequality for polynomials with real zeros”, Proc. Amer. Math. Soc., 93 (1985), 43–47 | DOI | MR | Zbl

[13] Borwein P., Computational excursions in analysis and number theory, CMS Books in Math./Ouvrages de Math. de la SMC, 10, Springer, New York, 2002 | MR

[14] Borwein P., Erdélyi T., “Markov–Bernstein-type inequalities for classes of polynomials with restricted zeros”, Constr. Approx., 10 (1994), 411–425 | DOI | MR | Zbl

[15] Borwein P., Erdélyi T., “Markov and Bernstein type inequalities in $L_p$ for classes of polynomials with constraints”, J. London Math. Soc. (2), 51 (1995), 573–588 | MR | Zbl

[16] Borwein P., Erdélyi T., “Upper bounds for the derivative of exponential sums”, Proc. Amer. Math. Soc., 123 (1995), 1481–1486 | DOI | MR | Zbl

[17] Borwein P., Erdélyi T., Polynomials and polynomial inequalities, Grad. Texts in Math., 161, Springer-Verlag, New York, NY, 1995 | MR

[18] Borwein P., Erdélyi T., “Müntz spaces and Remez inequalities”, Bull. Amer. Math. Soc. (N.S.), 32 (1995), 38–42 | DOI | MR | Zbl

[19] Borwein P., Erdélyi T., “Sharp extensions of Bernstein's inequality to rational spaces”, Mathematika, 43 (1996), 413–423, (1997) | MR

[20] Borwein P., Erdélyi T., “The full Müntz theorem in $C[0,1]$ and $L_1[0,1]$”, J. London Math. Soc. (2), 54 (1996), 102–110 | MR | Zbl

[21] Borwein P., Erdélyi T., “Newman's inequality for Müntz polynomials on positive intervals”, J. Approx. Theory, 85 (1996), 132–139 | DOI | MR | Zbl

[22] Borwein P., Erdélyi T., “The $L_p$ version of Newman's inequality for lacunary polynomials”, Proc. Amer. Math. Soc., 124 (1996), 101–109 | DOI | MR | Zbl

[23] Borwein P., Erdélyi T., “A sharp Bernstein-type inequality for exponential sums”, J. Reine Angew. Math., 476 (1996), 127–141 | MR | Zbl

[24] Borwein P., Erdélyi T., “The integer Chebyshev problem”, Math. Comp., 65 (1996), 661–681 | DOI | MR | Zbl

[25] Borwein P., Erdélyi T., “Generalizations of Müntz's theorem via a Remez-type inequality for Müntz spaces”, J. Amer. Math. Soc., 10 (1997), 327–349 | DOI | MR | Zbl

[26] Borwein P., Erdélyi T., “On the zeros of polynomials with restricted coefficients”, Illinois J. Math., 41 (1997), 667–675 | MR | Zbl

[27] Borwein P., Erdélyi T., “Pointwise Remez- and Nikolskii-type inequalities for exponential sums”, Math. Ann., 316 (2000), 39–60 | DOI | MR | Zbl

[28] Borwein P., Erdélyi T., “Markov- and Bernstein-type inequalities for polynomials with restricted coefficients”, Ramanujan J., 1 (1997), 309–323 | DOI | MR | Zbl

[29] Borwein P., Erdélyi T., “Littlewood-type problems on subarcs of the unit circle”, Indiana Univ. Math. J., 46 (1997), 1323–1346 | DOI | MR | Zbl

[30] Borwein P., Erdélyi T., “Markov–Bernstein type inequalities under Littlewood-type coefficient constraints”, Indag. Math. (N.S.), 11 (2000), 159–172 | DOI | MR | Zbl

[31] Borwein P., Erdélyi T., “Lower bounds for the merit factors of trigonometric polynomials from Littlewood classes”, J. Approx. Theory, 125 (2003), 190–197 | DOI | MR | Zbl

[32] Borwein P., Erdélyi T., “Nikolskii-type inequalities for shift invariant function spaces”, Proc. Amer. Math. Soc., 134 (2006), 3243–3246, (electronic) | DOI | MR | Zbl

[33] Borwein P., Erdélyi T., “Lower bounds for the number of zeros of cosine polynomials in the period: a problem of Littlewood”, Acta Arith., 128 (2007), 377–384 | DOI | MR | Zbl

[34] Borwein P., Erdélyi T., Kós G., “Littlewood-type problems on $[0,1]$”, Proc. London Math. Soc. (3), 79 (1999), 22–46 | DOI | MR | Zbl

[35] Borwein P., Erdélyi T., Zhang J., “Müntz systems and orthogonal Müntz–Legendre polynomials”, Trans. Amer. Math. Soc., 342 (1994), 523–542 | DOI | MR | Zbl

[36] Borwein P., Erdélyi T., Zhang J., “Chebyshev polynomials and Markov–Bernstein type inequalities for rational spaces”, J. London Math. Soc. (2), 50 (1994), 501–519 | MR | Zbl

[37] Borwein P., Erdélyi T., Littmann F., “Polynomials with coefficients from a finite set”, Trans. Amer. Math. Soc., 360:10 (2008), 5145–5154 | DOI | MR | Zbl

[38] Borwein P., Erdélyi T., Ferguson R., Lockhart R., “On the zeros of cosine polynomials: solution to a problem of Littlewood”, Ann. of Math. (2), 167 (2008), 1109–1117 | DOI | MR | Zbl

[39] Borwein P., Pinner C., Pritsker I., “Monic integer Chebyshev problem”, Math. Comp., 72 (2003), 1901–1916, (electronic) | DOI | MR | Zbl

[40] Boyd D., “On a problem of Byrnes concerning polynomials with restricted coefficients”, Math. Comp., 66 (1997), 1697–1703 | DOI | MR | Zbl

[41] Braess D., Nonlinear approximation theory, Springer Ser. Comput. Math., 7, Springer-Verlag, Berlin, 1986 | MR | Zbl

[42] Clarkson J. A., Erdős P., “Approximation by polynomials”, Duke Math. J., 10 (1943), 5–11 | DOI | MR | Zbl

[43] Conrey B., Granville A., Poonen B., Soundararajan K., “Zeros of Fekete polynomials”, Ann. Inst. Fourier (Grenoble), 50 (2000), 865–889 | MR | Zbl

[44] DeVore R. A., Lorentz G. G., Constructive approximation, Grundlehren Math. Wiss., 303, Springer-Verlag, Berlin, 1993 | MR | Zbl

[45] Ditzian Z., Lubinsky D., “Jackson and smoothness theorems for Freud weights in $L_p$ $(0

\le\infty)$”, Constr. Approx., 13 (1997), 99–152 | MR | Zbl

[46] Erdélyi T., “The Remez inequality on the size of polynomials”, Approximation Theory VI, Vol. I (College Station, TX, 1989), eds. C. K. Chui, L. L. Schumaker, J. D. Wards, Acad. Press, Boston, MA, 1989, 243–246 | MR

[47] Erdélyi T., “Markov-type estimates for certain classes of constrained polynomials”, Constr. Approx., 5 (1989), 347–356 | DOI | MR | Zbl

[48] Erdélyi T., “Estimates for the Lorentz degree of polynomials”, J. Approx. Theory, 67 (1991), 187–198 | DOI | MR | Zbl

[49] Erdélyi T., “Bernstein-type inequality for the derivatives of constrained polynomials”, Proc. Amer. Math. Soc., 112 (1991), 829–838 | DOI | MR | Zbl

[50] Erdélyi T., “Bernstein and Markov type inequalities for generalized nonnegative polynomials”, Canad. J. Math., 43 (1991), 495–505 | MR | Zbl

[51] Erdélyi T., “Remez-type inequalities on the size of generalized polynomials”, J. London Math. Soc. (2), 45 (1992), 255–264 | DOI | MR | Zbl

[52] Erdélyi T., “Remez-type inequalities and their applications”, J. Comput. Appl. Math., 47 (1993), 167–209 | DOI | MR | Zbl

[53] Erdélyi T., “Markov–Bernstein type inequalities for constrained polynomials with real versus complex coefficients”, J. Anal. Math., 74 (1998), 165–181 | DOI | MR | Zbl

[54] Erdélyi T., “Markov-type inequalities for constrained polynomials with complex coefficients”, Illinois J. Math., 42 (1998), 544–563 | MR | Zbl

[55] Erdélyi T., “Markov- and Bernstein-type inequalities for Müntz polynomials and exponential sums in $L_p$”, J. Approx. Theory, 104 (2000), 142–152 | DOI | MR | Zbl

[56] Erdélyi T., “The resolution of Saffari's phase problem”, C. R. Acad. Sci. Paris Sér. I Math., 331:10 (2000), 803–808 | MR | Zbl

[57] Erdélyi T., “On the zeros of polynomials with Littlewood-type coefficient constraints”, Michigan Math. J., 49 (2001), 97–111 | DOI | MR | Zbl

[58] Erdélyi T., “How far is an ultraflat sequence of unimodular polynomials from being conjugate-reciprocal?”, Michigan Math. J., 49 (2001), 259–264 | DOI | MR | Zbl

[59] Erdélyi T., “The phase problem of ultraflat unimodular polynomials: the resolution of the conjecture of Saffari”, Math. Ann., 321 (2001), 905–924 | DOI | MR | Zbl

[60] Erdélyi T., “Proof of Saffari's near-orthogonality conjecture for ultraflat sequences of unimodular polynomials”, C. R. Acad. Sci. Paris Sér. I Math., 333:7 (2001), 623–628 | MR | Zbl

[61] Erdélyi T., “The “full Clarkson–Erdős–Schwartz theorem” on the closure of non-dense Müntz spaces”, Studia Math., 155 (2003), 145–152 | DOI | MR | Zbl

[62] Erdélyi T., “Extremal properties of the derivatives of the Newman polynomials”, Proc. Amer. Math. Soc., 131 (2003), 3129–3134, (electronic) | DOI | MR | Zbl

[63] Erdélyi T., “On the real part of ultraflat sequences of unimodular polynomials: consequences implied by the resolution of the phase problem”, Math. Ann., 326 (2003), 489–498 | MR | Zbl

[64] Erdélyi T., “The “full Müntz theorem” revisited”, Constr. Approx., 21 (2005), 319–335 | DOI | MR | Zbl

[65] Erdélyi T., “Bernstein-type inequalities for linear combinations of shifted Gaussians”, Bull. London Math. Soc., 38 (2006), 124–138 | DOI | MR | Zbl

[66] Erdélyi T., “Markov–Nikolskii-type inequalities for exponential sums on finite intervals”, Adv. Math., 208 (2007), 135–146 | DOI | MR | Zbl

[67] Erdélyi T., “The Remez inequality for linear combinations of shifted Gaussians”, Math. Proc. Cambridge Philos. Soc. (to appear) | MR

[68] Erdélyi T., “Newman's inequality for increasing exponential sums”, Number Theory and Polynomials, London Math. Soc. Lecture Note Ser., 352, Cambridge Univ. Press, Cambridge, 2008, 127–141 | MR

[69] Erdélyi T., “Inequalities for exponential sums via interpolation and Turán-type reverse Markov inequalities”, Frontiers in Interpolation and Approximation, Pure Appl. Math. (Boca Raton), 282, Chapman Hall/CRC, Boca Raton, FL, 2007, 119–144 | MR

[70] Erdélyi T., “An improvement of the Erdős–Turán theorem on the distribution of zeros of polynomials”, C. R. Math. Acad. Sci. Paris, 346:5–6 (2008), 267–270 | MR | Zbl

[71] Erdélyi T., “Extensions of the Bloch–Pólya theorem on the number of real zeros of polynomials”, J. Théor. Nombres Bordeaux, 20:2 (2008), 281–287 | MR | Zbl

[72] Erdélyi T., Johnson W., “The “full Müntz theorem” in $L_p[0,1]$ for $0

\infty$”, J. Anal. Math., 84 (2001), 145–172 | DOI | MR | Zbl

[73] Erdélyi T., Szabados J., “On polynomials with positive coefficients”, J. Approx. Theory, 54 (1988), 107–122 | DOI | MR | Zbl

[74] Erdélyi T., Magnus A., Nevai P., “Generalized Jacobi weights, Christoffel functions, and Jacobi polynomials”, SIAM J. Math. Anal., 25 (1994), 602–614 | DOI | MR | Zbl

[75] Erdélyi T., Nevai P., “Lower bounds for derivatives of polynomials and Remez type inequalities”, Trans. Amer. Math. Soc., 349 (1997), 4953–4972 | DOI | MR | Zbl

[76] Erdélyi T., Máté A., Nevai P., “Inequalities for generalized nonnegative polynomials”, Constr. Approx., 8 (1992), 241–255 | DOI | MR | Zbl

[77] Erdélyi T., Szabados J., “On a generalization of the Bernstein–Markov inequality”, Algebra i analiz, 14:4 (2002), 36–53 ; St. Petersburg Math. J., 14:4 (2003), 563–576 | MR | Zbl

[78] Erdős P., “On extremal properties of the derivatives of polynomials”, Ann. of Math. (2), 41 (1940), 310–313 | DOI | MR | Zbl

[79] Erdős P., “Some unsolved problems”, Michigan Math. J., 4 (1957), 291–300 | DOI | MR

[80] Erdős P., Turán P., “On the distribution of roots of polynomials”, Ann. of Math. (2), 51 (1950), 105–119 | DOI | MR | Zbl

[81] Erőd J., “Bizonyos polinomok maximumának alsó korlátjáról”, Matematikai és Fizikai Lapok, 46 (1939), 83–84

[82] Frappier C., Quelques problèmes extrémaux pour les polynomes et les fonctions entières de type exponentiel, Ph. D. Dissertation, Univ. Montréal, 1982

[83] Freud G., Orthogonal polynomials, Pergamon Press, Oxford, 1971

[84] Güntürk G., “Approximation by power series with $\pm1$ coefficients”, Int. Math. Res. Not., 2005, no. 26, 1601–1610 | DOI | MR | Zbl

[85] Halász G., “Markov-type inequalities for polynomials with restricted zeros”, J. Approx. Theory, 101 (1999), 148–155 | DOI | MR | Zbl

[86] Hare K., Smyth C., “The monic integer transfinite diameter”, Math. Comp., 75 (2006), 1997–2019, (electronic) | DOI | MR | Zbl

[87] Hausdorff F., “Summationsmethoden und Momentfolgen. I”, Math. Z., 9 (1921), 74–109 | DOI | MR | Zbl

[88] Hua L. K., Introduction to number theory, Springer-Verlag, Berlin–New York, 1982 | MR

[89] Kac M., “On the average number of real roots of a random algebraic equation. II”, Proc. London Math. Soc. (2), 50 (1949), 390–408 | DOI | MR

[90] Kahane J. P., “Sur les polynômes à coefficients unimodulaires”, Bull. London Math. Soc., 12 (1980), 321–342 | DOI | MR | Zbl

[91] Körner T., “On a polynomial of Byrnes”, Bull. London Math. Soc., 12 (1980), 219–224 | DOI | MR | Zbl

[92] Konyagin S., “On a question of Pichorides”, C. R. Acad. Sci. Paris Sér I Math., 324 (1997), 385–388 | MR | Zbl

[93] Konyagin S. V., “O probleme Littlvuda”, Izv. AN SSSR. Ser. mat., 45:2 (1981), 243–265 ; Math. USSR-Izv., 18:2 (1982), 205–225 | MR | Zbl | DOI

[94] Konyagin S. V., Lev V. F., “Character sums in complex half-planes”, J. Théor. Nombres Bordeaux, 16:3 (2004), 587–606 | MR | Zbl

[95] Levenberg N., Poletsky E., “Reverse Markov inequality”, Ann. Acad. Sci. Fenn. Math., 27 (2002), 173–182 | MR | Zbl

[96] Littlewood J. E., “On the mean values of certain trigonometric polynomials”, J. London Math. Soc., 36 (1961), 307–334 | DOI | MR | Zbl

[97] Littlewood J. E., “On the real roots of real trigonometrical polynomials. II”, J. London Math. Soc., 39 (1964), 511–552 | DOI | MR

[98] Littlewood J. E., “On polynomials $\sum\pm z^m$ and $\sum e^{\alpha_mi}z^m$, $z=e^{\theta i}$”, J. London Math. Soc., 41 (1966), 367–376 | DOI | MR | Zbl

[99] Littlewood J. E., Some problems in real and complex analysis, D. C. Heath and Co., Lexington, MA, 1968 | MR | Zbl

[100] Littlewood J. E., Offord A. C., “On the number of real roots of a random algebraic equation. II”, Proc. Cambridge Philos. Soc., 35 (1939), 133–148 | DOI | Zbl

[101] Szabados J., Kroó A., “Constructive properties of self-reciprocal polynomials”, Analysis, 14 (1994), 319–339 | MR | Zbl

[102] Lorentz G. G., “The degree of approximation by polynomials with positive coefficients”, Math. Ann., 151 (1963), 239–251 | DOI | MR | Zbl

[103] Lorentz G. G., “Notes on approximation”, J. Approx. Theory, 56 (1989), 360–365 | DOI | MR | Zbl

[104] Lorentz G. G., Approximation of functions, 2nd ed., Chelsea Publ. Co., New York, 1986 | MR | Zbl

[105] Lorentz G. G., von Golitschek M., Makovoz Y., Constructive approximation. Advanced problems, Grundlehren Math. Wiss., 304, Springer-Verlag, Berlin, 1996 | MR | Zbl

[106] Milovanović G. V., Mitrinović D. S., Rassias Th. M., Topics in polynomials: extremal problems, inequalities, zeros, World Sci. Publ. Co., Inc., River Edge, NJ, 1994 | MR | Zbl

[107] McGehee O. C., Pigno L., Smith B., “Hardy's inequality and the $L_1$ norm of exponential sums”, Ann. of Math. (2), 113 (1981), 613–618 | DOI | MR | Zbl

[108] Mercer I. D., “Unimodular roots of special Littlewood polynomials”, Canad. Math. Bull., 49:3 (2006), 438–447 | MR | Zbl

[109] Mhaskar H. N., Introduction to the theory of weighted polynomial approximation, Ser. Approx. Decompos., 7, World Publ. Co., Inc., River Edge, NJ, 1996 | MR | Zbl

[110] Mhaskar H. N., “When is approximation by Gaussian networks necessarily a linear process?”, Neural Networks, 17 (2004), 989–1001 | DOI | Zbl

[111] Montgomery H. L., Ten lectures on the interface between analytic number theory and harmonic analysis, CBMS Regional Conf. Ser. in Math., 84, Amer. Math. Soc., Providence, RI, 1994 | MR | Zbl

[112] Müntz C., Über den Approximationsatz von Weierstrass, H. A. Schwartz Festschrift, Berlin, 1914

[113] Nazarov F. L., “Lokalnye otsenki eksponentsialnykh polinomov i ikh prilozheniya k neravenstvam tipa printsipa neopredelennosti”, Algebra i analiz, 5:4 (1993), 3–66 ; St. Petersburg Math. J., 5:4 (1994), 663–717 | MR | Zbl

[114] Newman D. J., “Derivative bounds for Müntz polynomials”, J. Approx. Theory, 18 (1976), 360–362 | DOI | MR | Zbl

[115] Newman D. J., Approximation with rational functions, CBMS Regional Conf. Ser. in Math., 41, Conf. Board of Math. Sci., Washington, DC, 1979 | MR | Zbl

[116] Nikolskii S. M., “Neravenstva dlya tselykh funktsii konechnoi stepeni i ikh primenenie v teorii differentsiruemykh funktsii mnogikh peremennykh”, Tr. Mat. in-ta AN SSSR, 38, 1951, 244–278 | MR | Zbl

[117] Odlyzko A., Poonen B., “Zeros of polynomials with $0,1$ coefficients”, Enseign. Math. (2), 39 (1993), 317–348 | MR | Zbl

[118] Petrushev P. P., Popov V. A., Rational approximation of real functions, Encyclopedia Math. Appl., 28, Cambridge Univ. Press, Cambridge, 1987 | MR | Zbl

[119] Pichorides S. K., “Notes on trigonometric polynomials”, Conference on Harmonic Analysis in Honor of Antoni Zygmund, Vol. I (Chicago, Ill., 1981), Wadsworth Math. Ser., Wadsworth, Belmont, CA, 1983, 84–94 | MR

[120] Rahman Q. I., Schmeisser G., Les inegalités de Markoff et de Bernstein, Sém. Math. Supér., 86, Presses Univ. Montréal, Montreal, QC, 1983 | MR | Zbl

[121] Rahman Q. I., Schmeisser G., Analytic theory of polynomials, London Math. Soc. Monogr. New Ser., 26, Oxford Univ. Press, Oxford, 2002 | MR | Zbl

[122] Remes E. J., “Sur une propriété extrémale des polynômes de Tchebyscheff”, Zap. Nauch.-issled. in-ta mat. i mekh. Khark. un-ta i Khark. mat. o-va (4), 13:1 (1936), 93–95 | Zbl

[123] Révész Sz., “Turán type reverse Markov inequalities for compact convex sets”, J. Approx. Theory, 141 (2006), 162–173 | DOI | MR | Zbl

[124] Queffélec H., Saffari B., “Unimodular polynomials and Bernstein's inequalities”, C. R. Acad. Sci. Paris Sér. I Math., 321 (1995), 313–318 | MR | Zbl

[125] Queffélec H., Saffari B., “On Bernstein's inequality and Kahane's ultraflat polynomials”, J. Fourier Anal. Appl., 2 (1996), 519–582 | DOI | MR | Zbl

[126] Saffari B., “The phase behavior of ultraflat unimodular polynomials”, Probabilistic and Stochastic Methods in Analysis, with Applications (Il Ciocco, 1991), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 372, Kluwer Acad. Publ., Dordrecht, 1992, 555–572 | MR

[127] Scheick J. T., “Inequalities for derivatives of polynomials of special type”, J. Approx. Theory, 6 (1972), 354–358 | DOI | MR | Zbl

[128] Schmidt E., “Zur Kompaktheit bei Exponentialsummen”, J. Approx. Theory, 3 (1970), 445–454 | DOI | MR | Zbl

[129] Schur I., “Untersuchungen über algebraische Gleichungen”, Sitz. Preuss. Akad. Wiss., Phys.-Math. Kl., 1933, no. 7–10, 403–428 | Zbl

[130] Sheil-Small T., Complex polynomials, Cambridge Stud. Adv. Math., 75, Cambridge Univ. Press, Cambridge, 2002 | MR | Zbl

[131] Somorjai G., “A Müntz-type problem for rational approximation”, Acta. Math. Acad. Sci. Hungar., 27 (1976), 197–199 | DOI | MR | Zbl

[132] Solomyak B., “On the random series $\sum\pm\lambda^n$ (Erdős problem)”, Ann. of Math. (2), 142 (1995), 611–625 | DOI | MR | Zbl

[133] Szegő G., “Bemerkungen zu einem Satz von E. Schmidt uber algebraische Gleichungen”, Sitz. Preuss. Akad. Wiss., Phys.-Math. Kl., 1934, no. 8, 86–98 | Zbl

[134] Szegő G., Zygmund A., “On certain mean values of polynomials”, J. Anal. Math., 3 (1954), 225–244 | DOI | MR | Zbl

[135] Totik V., Varjú P., “Polynomials with prescribed zeros and small norm”, Acta Sci. Math. (Szeged), 73 (2007), 593–611 | Zbl

[136] Turán P., “Über die Ableitung von Polynomen”, Compositio Math., 7 (1939), 89–95 | MR | Zbl

[137] Turán P., On a new method of analysis and its applications, Wiley, New York, NY, 1984 | MR | Zbl

[138] Wu Q., “A new exceptional polynomial for the integer transfinite diameter of $[0,1]$”, J. Théor. Nombres Bordeaux, 15 (2003), 847–861 | MR | Zbl