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Transfinite diameter, Chebyshev constant, logarithmic capacity. (Diámetro transfinito, constante de Chebyshev, capacidad logarítmica.) (Spanish) Zbl 07871148


MSC:

30C85 Capacity and harmonic measure in the complex plane

References:

[1] J. M. Almira y N. del Toro, Sobre aproximación con polinomios de coeficientes enteros,La Gaceta de la RSME2(2003), no. 2, 377-403. · Zbl 1358.41002
[2] C. Beltrán, F. Marcellán y A. Martínez-Finkelshtein, Algunas propiedades extremales de las raíces de polinomios ortogonales,La Gaceta de la RSME21(2018), no. 2, 345-366. · Zbl 1403.65022
[3] E. Bendito, A. Carmona y A. M. Encinas, Algunas aplicaciones de la teoría del potencial,XV Congreso de Ecuaciones Diferenciales y Aplicaciones, V Congreso de Matemática Aplicada (Vigo, 23-26 septiembre 1997), vol. 2, 1045-1050, Universidad de Vigo, 1998, . · Zbl 0960.31500
[4] P. Borwein y T. Erdélyi, The integer Chebyshev problem,Math. Comp.65 (1996), no. 214, 661-681. · Zbl 0859.11044
[5] J. I. Burgos Gil y R. Menares,Equidistribución, Teoría del potencial y Aplicaciones Aritméticas, 2019.http : / / www . mat . uc . cl /  rmenares / Equidistribucion.pdf
[6] M. I. Chlodovsky, Une remarque sur la représentation des fonctions continues par des polynomes à coefficients entiers,Mat. Sb.32(1925), 472-474. · JFM 51.0210.04
[7] H. G. Diamond, Elementary methods in the study of the distribution of prime numbers,Bull. Amer. Math. Soc. (N.S.)7(1982), no. 3, 553-589. · Zbl 0505.10021
[8] M. Fekete, Über die Verteilung der Wurzeln bei gewissen algebraischen Gleichungen mit ganzzahligen Koeffizienten,Math. Z.17(1923), 228-249. · JFM 49.0047.01
[9] Le Baron O. Ferguson,Approximation by polynomials with integral coefficients, Mathematical Surveys, 17, American Mathematical Society, Providence, R.I., 1980. · Zbl 0441.41003
[10] D. Hilbert, Ein Beitrag zur Theorie des Legendre’schen Polynoms,Acta Math. 18(1894), 155-159. · JFM 25.0817.02
[11] E. Hille, Remarks on transfinite diameters,General Topology and its relations to Modern Analysis and Algebra, (Proceedings of the symposium held in Prague in September 1961), 211-220, Academia Publishing House of the Czechoslovak Academy of Sciences, Prague, 1962.http://dml.cz/dmlcz/700913 · Zbl 0113.06203
[12] S. Kakeya, On approximate polynomials,Tôhoku Math. J.6(1914/1915), 182-186. · JFM 45.0327.04
[13] L. V. Kantorovic, Some remarks on the approximation of functions by means of polynomials with integral coefficients,Izv. Akad. Nauk SSSR Ser. Mat.9 (1931), 1163-1168 (en ruso). · Zbl 0003.39102
[14] M. Klein, Estimates for the transfinite diameter with applications to conformal mapping,Pacific J. Math.22(1967), no. 2, 267-279. · Zbl 0185.32803
[15] A. I. Markushevich,Teoría de las funciones analíticas (Curso breve), Urmo, S. A. Ediciones, 1977.
[16] H. L. Montgomery,Ten lectures on the interface between analytic Number Theory and Harmonic Analysis, CBMS Regional Conference Series in Mathematics, 84, American Mathematical Society, Providence, R.I., 1994. · Zbl 0814.11001
[17] J. Pál, Zwei kleine Bemerkungen,Tôhoku Math. J.6(1914/1915), 42-43. · JFM 45.0634.04
[18] I. C. Pérez Izquierdo,Asintótica de polinomios extremales de Sobolev, Tesis Doctoral, Universidad de La Habana, 2006.
[19] T. Ransford,Potential theory in the complex plane, Cambridge Univ. Press, Cambridge, 1995. · Zbl 0828.31001
[20] E. B. Saff, Logarithmic potential theory with applications to approximation theory,Surv. Approx. Theory5(2010), 165-200. · Zbl 1285.30020
[21] M. Tsuji,Potential theory in modern function theory, Maruzen, Tokio, 1959. Francisco Luquin, Departamento de Matemáticas, Universidad del País Vasco / Euskal Herriko Unibertsitatea Correo electrónico:francisco.luquin@ehu · Zbl 0087.28401
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