PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2004 | 2 | 3 | 448-477
Tytuł artykułu

A survey of certain results on strong approximation by orthogonal series

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This is a survey of results in a particular direction of the theory of strong approximation by orthogonal series, related mostly with author's contributions to the subject.
Wydawca
Czasopismo
Rocznik
Tom
2
Numer
3
Strony
448-477
Opis fizyczny
Daty
wydano
2004-06-01
online
2004-06-01
Twórcy
Bibliografia
  • [1] G. Alexits:Konvergenzprobleme der Orthogonalreihen, Akadémiai Kiadó, Budapest, 1960.
  • [2] G. Alexits: “Sur les bornes de la théorie, de l'approximation des fonctions continues par polynomes”,Magyar. Tud. Akad. Mat. Kut. Int. Közl., Vol. 8, (1963), pp. 329–340.
  • [3] G. Alexits and D. Králik: “Über den Annäherungsgrad der Approximation im starken Sinne von stetigen Funktionen”,Magyar Tud. Akad. Mat. Kut. Int. Közl., Vol. 8, (1963), pp. 317–327.
  • [4] G. Alexits and D. Králik: “Some remarks on the approximation in strong sense”,Analysis Math., Vol. 1, (1975), pp. 3–8. http://dx.doi.org/10.1007/BF01905108
  • [5] S. Bernstein: “Sur l'ordre de la meilleure approximation des fonctions continues par des polynomes de degré donné”,Mémoires Acad. Roy. Belgique, Vol. 4, (1912), pp. 1–104.
  • [6] K. Endl: “Ein Beitrag zur Theorie der starken Summierbarkeit mit einer Anwendung auf Orthonormalreihen”,Acta Sci. Math., Vol. 43, (1981), pp. 27–35.
  • [7] K. Endl and L. Leindler: “On the strong summability and approximation of orthogonal series with large exponent”,Analysis, Vol. 3, (1983), 123–134.
  • [8] L. Fejér: “Untersuchungen über Fouriersche Reihen”,Math. Annalen, Vol. 58, (1904), pp. 501–569.
  • [9] T.M. Flett: “Some more theorems concerning the absolute summability of Fourier series and power series”,Proc. London Math. Soc., Vol. 8, (1958), Vol. 357–387.
  • [10] G.H. Hardy:Divergent series, Clarendon Press, Oxford, 1956.
  • [11] G.H. Hardy and J.E. Littlewood: “Sur la série de Fourier d'une fonction à carré sommable”,Comptes Rendus, Vol. 28, (1913), pp. 1307–1309.
  • [12] W. Henrich: “Starke Approximation von Orthogonalreihen mit Cesàroverfahren”,Acta Sci. Math., Vol. 54, (1990), pp. 305–312.
  • [13] P.S. Kantawala, S.R. Agrawal and C.M. Patel: “On strong approximation of Nörlund and Euler means of orthogonal series”,Indian Journal of Math., Vol. 33, (1991), pp 99–117.
  • [14] L. Leindler: “Über die sehr starke Riesz-Summierbarkeit der Orthogonalreihen und Konvergenz lückenhafter orthogonalreihen”,Acta Math. Acad. Sci. Hung., Vol. 13, (1962), pp. 401–414. http://dx.doi.org/10.1007/BF02020805
  • [15] L. Leindler: “Über die de la Vallée Poussinschen Mittel allgemeiner Orthogonalreihen”,Publ. Math. Debrecen, Vol. 10, (1963), pp. 274–282.
  • [16] L. Leindler: “Über die Rieszschen Mittel allgemeiner Orthogonalreihen”,Acta Sci. Math., Vol. 24, (1963), pp. 129–138.
  • [17] L. Leindler: “Über die de la Vallée Poussinsche Summierbarkeit allgemeiner Orthogonalreihen”,Acta Math. Acad. Sci. Hung., Vol. 16, (1965), pp. 375–387. http://dx.doi.org/10.1007/BF01904844
  • [18] L. Leindler: “On summability of Fourier series”,Acta Sci. Math., Vol. 29, (1968), pp. 147–162.
  • [19] L. Leindler: “On the strong approximation of orthogonal series”,Acta Sci. Math., Vol. 32, (1971), pp. 41–50.
  • [20] L. Leindler: “On the strong approximation of orthogonal series”,Acta Sci. Math., Vol. 37, (1975), pp. 87–94.
  • [21] L. Leindler: “On the very strong approximation of orthogonal series”,Mitt. Math. Sem. Giessen, Vol. 147, (1981), pp. 131–140.
  • [22] L. Leindler: “On the strong summability and approximation of orthogonal series”,Acta Math. Acad. Sci. Hungar., Vol. 37, (1981), pp. 245–254. http://dx.doi.org/10.1007/BF01904886
  • [23] L. Leindler: “On the strong and very strong summability and approximation of orthogonal series by generalized Abel method”,Studia Sci. Math. Hung., Vol. 16, (1981), pp. 35–43.
  • [24] L. Leindler: “On the extra strong approximation of orthogonal series”,Analysis Math., Vol. 8, (1982), pp. 125–133. http://dx.doi.org/10.1007/BF01911334
  • [25] L. Leindler: “On the strong approximation of orthogonal series with large exponent”,Analysis Math., Vol. 8, (1982), pp. 173–179. http://dx.doi.org/10.1007/BF02199926
  • [26] L. Leindler: “Limit cases in the strong approximation of orthogonal series”,Acta Sci. Math., Vol. 48, (1985), pp. 269–284.
  • [27] L. Leindler:Strong approximation by Fourier series, Akadémiai Kiadó, Budapest, 1985.
  • [28] L. Leindler: “On the generalized strong de la Vallée Poussin approximation”,Acta Sci. Math., Vol. 56, (1992), pp. 83–88.
  • [29] L. Leindler: “A note on the strong de la Vallée Poussin approximation”,Acta Sci. Math., Vol. 56, (1992), pp. 287–291.
  • [30] L. Leindler: “On strong approximation by Cesàro means of negative order”,Acta Sci. Math., Vol. 56, (1992), pp. 293–303.
  • [31] L. Leindler: “Some results on strong approximation by orthogonal series”,Acta Sci. Math., Vol. 58, (1993), pp. 127–141.
  • [32] L. Leindler: “A note on the relation between ordinary and strong approximation of orthogonal series”,Acta Math. Hungar., Vol. 63(4), (1994), pp. 361–370. http://dx.doi.org/10.1007/BF01874461
  • [33] L. Leindler: “On extensions of some theorems of Flett. I”,Acta Math. Hungar., Vol. 64, (1994), pp. 215–229.
  • [34] L. Leindler: “A note on the relation between ordinary and strong approximation of orthogonal series”,Acta Math. Hungar., Vol. 63, (1994), pp. 361–370. http://dx.doi.org/10.1007/BF01874461
  • [35] L. Leindler: “General results on strong approximation by Cesàro means of negative order”,Acta Math. Hungar., Vol. 66, (1995), pp. 61–82. http://dx.doi.org/10.1007/BF01874354
  • [36] L. Leindler and A. Meir: “General Results on strong approximation by orthogonal series”,Acta Sci. Math., Vol. 55, (1991), pp. 317–331.
  • [37] L. Leindler and A. Meir: “An additional note on strong approximation by orthogonal series”,Acta Sci. Math., Vol. 56, (1992), pp. 89–95.
  • [38] L. Leindler and H. Schwinn: “On the strong and extra strong approximation of orthogonal series”,Acta Sci. Math., Vol. 45, (1983), pp. 293–304.
  • [39] J. Marcinkiewicz: “Sur l'interpolation”,Studia Math., Vol. 6, (1936), pp. 1–17, 67–81.
  • [40] J. Meder: “On very strong Riesz-summability of orthogonal series”,Studia Math., Vol. 20, (1961), pp. 285–300.
  • [41] D. Menchoff: “Sur les séries de fonctions orthogonales bornées dans leur ensemble”,Recueil Math. Moscou (Math. Sbornik), Vol. 3, (1938), pp. 103–118.
  • [42] F. Móricz: “A note on the strongT-summation of orthogonal series”,Acta Sci. Math. (Szeged), Vol. 30, (1969), pp. 69–76.
  • [43] F. Móricz: “Approximation by partial sums and Cesàro means of multiple orthogonal series,”Tôhoku Math. Journ., Vol. 35, (1983), pp. 519–539.
  • [44] F. Móricz: “Approximation Theorems for Double Orthogonal Series, II”,Jour. of Approx. Theory, Vol. 51, (1987), pp. 372–382. http://dx.doi.org/10.1016/0021-9045(87)90045-1
  • [45] F. Móricz: “Strong approximation by rectangular partial sums of double orthogonal series”,Analysis Math., Vol. 13, (1987).
  • [46] L. Rempulska: “On the (A, p)-summability of orthonormal series”,Demonstratio Math., Vol. 13, (1980), pp. 919–925.
  • [47] F. Schipp: “On the strong approximation by the partial sums of the Walsh-Fourier series”,MTA III. Osztály Közleményei, Vol. 19, (1969), pp. 101–111 (in Hungarian with English Summary).
  • [48] H.-J. Schmeisser and W. Sickel:Some remarks on strong approximation by Cesàro means, Approximation and Function Spaces, Banach Center Publications, Warsaw, Vol. 22, 1989, 363–375.
  • [49] H. Schwinn: “On strong approximation of orthogonal series”,Acta Sci. Math., Vol. 60, (1995), pp. 609–618.
  • [50] G. Sunouchi: “On the strong summability of orthogonal series”,Acta Sci. Math. (Szeged), Vol. 27, (1966), pp. 71–76.
  • [51] G. Sunouchi: “Strong approximation by Fourier series and orthogonal series”,Indian J. Math., Vol. 9, (1967), pp. 237–246.
  • [52] I. Szalay:On the strong approximation of orthogonal series, Constructive Function Theory '77, Sofia, 1980, pp.505–510.
  • [53] I. Szalay:On the generalized absolute Cesàro-summability and the strong approximation of orthogonal series, Constructive Function Theory '81, Sofia, 1983, pp. 543–550.
  • [54] R. Taberski: “On the strong de la Vallée Poussin means for Fourier-Chebyshev series”,Annales Soc. Math. Polonae, Vol. 36, (1996), pp. 235–245.
  • [55] K. Tandori: “Über die orthogonalen Funktionen. IV (Starke Summation)”,Acta Sci. Math. (Szeged), Vol. 19, (1958), pp. 18–25.
  • [56] V. V. Zhuk:Strong approximation of periodic functions, Leningrad Univ., Leningrad, 1989.
  • [57] O. A. Ziza:Summability of Orthogonal Series, USSR, Moscow, 1999 (in Russian with English summary).
  • [58] A. Zygmund: “Sur l'application de la première moyenne arithmétique dans la théorie des séries orthogonales”,Fund. Math., Vol. 10, (1927), pp. 356–362.
  • [59] A. Zygmund: “On the convergence and summability of power series on the circle of convergence”,Proc. London Math. Soc., Vol. 47, (1941), pp. 326–350.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_BF02475239
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.