×
Turán, Pál

On some open problems of approximation theory. (English) Zbl 0454.41001

J. Approximation Theory 29, 23-89 (1980).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0454.41001

Cited in 26 Reviews
Cited in 47 Documents

MSC:

41-02 Research exposition (monographs, survey articles) pertaining to approximations and expansions
41A05 Interpolation in approximation theory
41A20 Approximation by rational functions
42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
01A75 Collected or selected works; reprintings or translations of classics

Keywords:

orthogonal polynomial theory; Lagrange interpolation; Hermite interpolation; Hermite-Birkhoff interpolation
PDF BibTeX XML Cite
\textit{P. Turán}, J. Approx. Theory 29, 23--89 (1980; Zbl 0454.41001)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] Askey, R, Mean convergence of orthogonal series and Lagrange interpolation, Acta math. acad. sci. hungar., 23, 71-85, (1972) · Zbl 0253.41003
[2] Balázs, J; Turán, P, Notes on interpolation, III, Acta math. acad. sci. hungar., 9, 195-214, (1958) · Zbl 0085.05104
[3] Balázs, J; Turán, P, Notes on interpolation, XI, Acta math. acad. sci. hungar., 16, 215-220, (1965) · Zbl 0142.31203
[4] Bernstein, S, Sur l’ordre de la meilleure approximation des fonctions continues par des polynômes de degré donné, Mem. acad. belgique (2), 4, 1-13, (1912) · JFM 45.0633.03
[5] Bernstein, S, Sur la limitation des valeurs d’un polynôme, Bull. acad. sci. URSS, 8, 1025-1050, (1931) · JFM 57.1427.06
[6] Berman, D.L, On the convergence of interpolation tables on the Jacobi-zeros and ±1, Izv. vysš. Učebn. zaved., 10, No. 137, 14-22, (1973) · Zbl 0268.42003
[7] Egerváry, E; Turán, P, Notes on interpolation, V, Acta math. acad. sci. hungar., 9, 259-267, (1958) · Zbl 0085.05203
[8] Erdös, P; Feldheim, E, Sur le mode de convergence pour l’interpolation de Lagrange, C. R. acad. sci. Paris, 203, 913-915, (1936) · JFM 62.0303.01
[9] Erdös, P; Turán, P, On interpolation, I, Ann. of math., 38, 142-155, (1937) · JFM 63.0233.03
[10] Erdös, P; Turán, P, On interpolation, II, Ann. of math., 39, 702-724, (1938) · JFM 64.0247.01
[11] Erdös, P; Turán, P, On interpolation, III, Ann. of math., 41, 510-553, (1940) · JFM 66.0272.01
[12] Edös, P; Turán, P, On uniformly dense distribution of certain sequences of points, Ann. of math., 41, 162-173, (1940) · JFM 66.0347.01
[13] Erdös, P; Turán, P, On the role of the lebesque-functions in the theory of the Lagrange interpolation, Acta math. acad. sci. hungar., 6, 47-66, (1955) · Zbl 0064.30101
[14] Erdös, P, Problems and results in the theory of interpolation, I, Acta math. acad. sci. hungar., 9, 381-388, (1958) · Zbl 0083.29001
[15] Erdös, P; Turán, P, An extremal problem in the theory of interpolation, Acta math. acad. sci. hungar., 12, 221-234, (1961) · Zbl 0098.27102
[16] Erdös, P, On the distribution of the roots of orthogonal polynomials, () · JFM 68.0143.01
[17] Faber, G, Über die interpolatorische darstellung stetiger funktionen, Jber. Deutsch. math. verein., 23, 190-210, (1914) · JFM 45.0381.04
[18] Fejér, L, Über interpolation, Gött. nachr., 1-16, (1916) · JFM 46.0419.01
[19] Fejér, L, Interpolation und konforme abbildung, Gött. nachr., 319-331, (1918) · JFM 46.0517.02
[20] Fejér, L, Die abschätzung eines polynoms in einem intervalle, wenn schranken für seine werte und ersten ableitungswerte in einzelen punkten des intervalles gegeben sind, und ihre anwendung auf die konvergenz hermitescher interpolationsreihen, Math. Z., 32, 426-457, (1930) · JFM 56.0112.03
[21] Fejér, L, Mechanische quadraturen mit positiven cotesschen zahlen, Math. Z., 37, 287-309, (1933) · JFM 59.0261.03
[22] Frenkel-Fertig, M, Sur une classe de polynômes généralisant des polynômes de Legendre, Acta. math. acad. sci. hungar., 17, 457-459, (1966) · Zbl 0143.08701
[23] Freud, G, Über die lebesgueschen funktionen der lagrangeschen interpolation, Acta math. acad. sci. hungar., 4, 132-147, (1953) · Zbl 0051.04804
[24] Freud, G, Über die konvergenz des Hermite-fejérschen interpolationsverfahrens, Acta math. acad. sci. hungar., 5, 109-127, (1954) · Zbl 0055.05906
[25] Freud, G, Über die approximation reeller funktionen durch rationale gebrochene funktionen, Acta math. acad. sci. hungar., 17, 313-324, (1966) · Zbl 0165.38802
[26] Freud, G; Vértesi, P, A new proof of A. F. Timan’s approximation theorem, Studia sci. math. hungar., 2, 403-414, (1967) · Zbl 0182.39301
[27] Freud, F; Vértesi, P, On rational approximation of absolutely continuous functions, Studia sci. math. hungar., 3, 383-386, (1968) · Zbl 0165.38901
[28] Grünwald, G, Über divergenzerscheinungen der lagrangeschen interpolationspolynome, Acta litt. sci., 7, 207-221, (1935) · JFM 61.1129.02
[29] Grünwald, G, Über divergenzerscheinungen der lagrangeschen interpolationspolynome stetiger funktionen, Ann. of math., 37, 908-918, (1936) · JFM 62.1192.02
[30] Grünwald, G; Turán, P, Über interpolation, Ann. scuola norm. sup. Pisa, 137-146, (1938) · JFM 64.0248.01
[31] Grünwald, G, On the theory of interpolation, Acta math., 75, 219-245, (1942) · Zbl 0028.05001
[32] Hahn, H, Über das interpolationsproblem, Math. Z., 1, 115-142, (1918) · JFM 46.0426.01
[33] Kalmár, L, On interpolation, Mat. fiz. lapok, 120-149, (1927)
[34] Kis, O, On trigonometric (0, 2) interpolation, Acta math. acad. sci. hungar., 11, 255-276, (1960) · Zbl 0103.28703
[35] Kis, O; Vértesi, P, On a new procedure of interpolation, Ann. univ. sci. Budapest. sect. math., 10, 117-128, (1967)
[36] Makai, E; Turán, P, Hermite-expansion and distribution of zeros of polynomials, Publ. math. inst. hung. acad. sci. A, 8, 157-164, (1963) · Zbl 0123.26402
[37] Marcinkiewicz, I, Sur la divergence des polynômes d’interpolation, Acta sci. math. (Szeged), 8, 131-135, (1937) · JFM 63.0233.02
[38] Meir, A; Sharma, A; Tzimbalario, J, Hermite-Fejér type interpolation processes, Analysis math., 1, 121-129, (1975) · Zbl 0315.41001
[39] Merriman, G.M, Concerning sets of polynomials orthogonal simultaneously on several circles, Bull. amer. math. soc., 44, 57-69, (1938) · Zbl 0018.25203
[40] Newman, D.J, Rational approximation to \(¦x¦\), Mich. math. J., 11, 11-14, (1964) · Zbl 0138.04402
[41] Popov, V.A, On the rational approximation of functions of the class Vr, Acta math. acad. sci. hungar., 25, 61-65, (1974) · Zbl 0276.41007
[42] Rahman, Q.I; Schmeisser, S; Turán, P, On a phenomenon concerning (0, 2) interpolation, Period. math. hungar., 9, 163-171, (1978) · Zbl 0401.41003
[43] Révész, G, On the approximation of the function ex by polynomials, Math. lapok, 12, 222-231, (1960)
[44] Somorjai, G, A Müntz-type problem for rational approximation, Acta math. acad. sci. hungar., 27, 197-199, (1976) · Zbl 0333.41012
[45] Specht, W, Algebraische gleichungen mit reellen oder komplexen koeffizienten, (), No. 3 · Zbl 0082.24503
[46] Steklov, V.A, On the approximative calculation of the integrals by mechanical quadrature, Izv. akad. nauk (6), 10, 169-186, (1916)
[47] Surányi, J; Turán, P, Notes on interpolation, I, Acta math. acad. sci. hungar, 6, 67-80, (1955) · Zbl 0064.30005
[48] Szabados, J, On the convergence of the interpolatory quadrature procedures in certain classes of functions, Acta math. acad. sci. hungar., 18, 97-111, (1967) · Zbl 0193.02603
[49] Szabados, J, Negative results in the theory of rational approximation, Studia sci. math. hungar., 2, 385-390, (1967) · Zbl 0183.05804
[50] Szabados, J, Rational approximation in certain classes of functions, Acta math. acad. sci. hungar., 19, 81-85, (1968) · Zbl 0175.06101
[51] Szabados, J, Rational approximation in the complex unit circle, Ann. univ. sci. Budapest. sect. math., 11, 105-108, (1968) · Zbl 0169.40402
[52] Szabados, J, On a problem of interpolation for the unit circle of the complex plane, Mat. lapok., 23, 297-300, (1972)
[53] Szász, P, On quasi-Hermite-Féjer interpolation, Acta math. acad. sci. hungar., 10, 413-439, (1959) · Zbl 0091.05704
[54] Szegö, G, Über gewisse interpolationspolynome, die zu den jacobischen und laguerreschen abszissen gehoren, Math. Z., 35, 573-602, (1932) · Zbl 0005.01302
[55] Szegö, G, Concerning sets of polynomials orthogonal simultaneously on several circles, Bull. amer. math. soc., 45, 129-132, (1939) · JFM 65.0286.02
[56] Szegö, G, Orthogonal polynomials, () · JFM 65.0278.03
[57] Szüsz, P; Turán, P, On the constructive theory of functions, I, Publ. math. inst. hung. acad. sci. A, 9, 495-502, (1964) · Zbl 0163.30502
[58] Szüsz, P; Turán, P, A konstruktive függvénytan egy ujabb irányáról, Magyar tud. akad. mat. fiz. oszt. Közl., 16, 1, 33-46, (1966)
[59] Turán, P, On the theory of mechanical quadrature, Acta sci. math. (Szeged), 12, 30-37, (1950) · Zbl 0041.44417
[60] Turán, P, A remark on Hermite-Fejér interpolation, Ann. univ. sci. Budapest. sect. math., 3-4, 369-377, (1960-1961) · Zbl 0103.28701
[61] Turán, P, On the approximation of piecewise analytic functions by rational functions, (), 269-299, Erevan
[62] Turán, P, On orthogonal polynomials, Analysis math., 1, 297-312, (1975) · Zbl 0331.42006
[63] Vértesi, P, On a problem of P. Turán, Canad. math. bull., 18, 283-288, (1975) · Zbl 0316.41002
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.