Articles On HAT


The following are papers concerning various topics in the history of approximation theory. Some of these papers are linked. If you have problems with the links, please let us know. Some of these papers are given as pdf files. For them you will need an appropriate Adobe Acrobat reader which you probably have. Otherwise go to Adobe.


  • Akhiezer, N. I., Academician S. N. Bernstein and his Work on the Constructive Theory of Functions (in Russian), Izdat. Harkov. Gosudarstv. Univ., Kharkov, 1955; translated into German as Das Akademiemitglied S. N. Bernstein und seine Arbeiten zur konstruktiven Funktionentheorie, translated and with a preface by Ralitza K. Kovacheva and Heinz H. Gonska. in Mitt. Math. Sem. Giessen No. 240 (2000), xiv + 97 pages. The original is an expanded form of the survey paper by N. I. Akhiezer with the same title which appeared in Uspekhi Mat. Nauk (N.S.) 6 (1951), no. 1(41), 3-67, which was written by Akhieser on the occasion of Bernstein’s 70th birthday.
  • Akhiezer, N. I., List of Publications. A list of publications of Naum Il’ich Akhiezer. We do not know how exact this list is.
  • Aleksandrov, P. S., N. I. Akhiezer, B. V. Gnedenko, and A. N. Kolmogorov, Sergei Natanovich Bernstein: Obituary, (in Russian Uspekhi Mat. Nauk 24 (3) (1969), 211-218; translation in Russian Math. Surveys 24 (3) (1969), 169-176.
  • Anderson, J. M., Obituary. The short obituary to J. Milne Anderson that appeared in Constructive Approximation 43 (2) (2016).
  • Andreev, A., V. I. Berdyshev, B. Bojanov, B. S Kashin, S. V. Konyagin, S. M. Nikolskii, K. I. Oskolkov, P. Petrushev, Bl. Sendov, S. A. Telyakovskii, and V. N. Temlyakov, In memory of Sergei Borisovich Stechkin [1920-1995], East J. Approx. 2 (1996), 131-133.
  • Aptekarev, A. I., G. López Lagomasino, E. B. Saff, V. Totik, and H. Stahl, Andrei Aleksandrovich Gonchar (on his 80th birthday), Uspekhi Mat. Nauk 66 (2011), 197-204. English transl. in Russian Math. Surveys 66 (2011), 1209-1216, see here.
  • Askey, R. A., and P. Nevai, Gabor Szegö: 1895–1985 , Math. Intelligencer 18, 3 (1996), 10-22, (for those with access) and in Hungarian, Mat. Lapok 3 (1993), 13-32.
  • Babich, V. M., A. M. Vershik, S. V. Videnskii, O. L. Vinogradov, I. K. Daugavet, N. Yu. Dodonov, V. V. Zhuk, B. M. Makarov, A. N. Podkorutov, Yu. G. Reshetnyak, M. A. Skopina, V. L. Fainshmidt, V. P. Havin, and N. A. Shirokov, Garal’d Isidorovich Natanson. (Russian) Uspekhi Mat. Nauk59 (2004), no. 4 (358),
    181-185; translation in Russian Math. Surveys 59 (2004), no. 4, 771-776, in English (for those with access).
  • Basharin, G. P., A. N.Langville and V. A. Naumov, The life and work of A.A. Markov, Linear Algebra and its Applications 386(2004) 3–26. This article should be read with some caution, according to its review in Zentralblatt Math. For those with access, this article may be viewed at Science Direct.
  • Boas, R. P., Extremal problems for polynomials, Amer. Math. Monthly 85 (1978), 473-475. A short pleasant expository note about the origins of the Markov inequality. This article may be viewed at JSTOR.
  • Bogoljubov, A. N., A. T. Grigorʹjan, G. I. Drinfelʹd, and A. P. Juškevič, Ja. L. Geronimus (on the occasion of his seventy-fifth birthday), (Russian) Voprosy Istor. Estestvoznan. i Tehn. Vyp. 2(43) (1973), 71-72.
  • Bolibrukh, A. A., A. G. Vitushkin, V. S. Vladimirov, E. F. Mischenko, S. P. Novikov, Yu. S. Osipov, A. G. Sergeev, P. L. Ul’yanov, L. D. Fadeev, and E. M. Chirka, Andrei Aleksandrovich Gonchar (on his 70th birthday), Uspekhi Mat. Nauk 57 (2001), 185–190. English transl. in Russian Math. Surveys 57 (2001), 191–198, see here.
  • de Boor, C., and A. Pinkus, The B-spline recurrence relations of Chakalov and Popoviciu, J. Approx. Theory 124 (2003), 115-123. This article may be viewed at Science Direct.
  • Borwein, P., and T. Erdélyi, Polynomials and Polynomial Inequalities, Springer-Verlag, New York, 1995. Contains a great deal of information on the history of approximation theory scattered throughout the text.
  • Braess, D. Helmut Werner, Computing 36 (1986), 181-182. For those with access, this article can be found here.
  • Braess, D., and R. Schaback, Helmut Werner, Jahresbericht DMV 89 (1987), 179-195. This article can be found in this issue of the Jahresbericht. (The article starts on page 39 of this pdf file.)
  • Brezinski, C., Historical Perspective on Interpolation, Approximation and Quadrature, in Handbook of Numerical Analysis, Volume III, eds. P. G. Ciarlet and J. L. Lions, p. 3-46, North Holland, 1994.
  • Brudnyi, Y., An excerpt concerning Timan’s life from: Timan’s type result on approximation by algebraic polynomials, in Operator Theory, Advances and Applications, Vol.98, Birkhäuser Verlag, Basel, 1997, pp. 92-101.
  • Bruins, E. M., On the history of approximation, in Constructive Function Theory ’77, Sofia, 1980, 275-280.
  • Burkill, J. C., Charles-Joseph de la Vallée Poussin, J. London Math. Soc. 39 (1964), 165-175.
  • Butzer, P. L., An outline of the life and work of E. B. Christoffel (1829-1900), Historia Math. 8 (1981), 243-276. For those with access, this article may be viewed at Science Direct.
  • Butzer, P. L., A retrospective on 60 years of approximation theory and associated fields, J. Approx. Theory, 160 (2009), 3-18. For those with access, this article may be viewed at Science Direct.
  • Butzer, P., and F. Jongmans, P. L. Chebyshev (1821-1894), a guide to his life and work, J. Approx. Theory 96 (1999), 111-138. For those with access, this article may be viewed at Science Direct.
  • Butzer, P. L., and F. Jongmans, P. L. Chebyshev (1821-1894) and his contacts with Western European scientists, Historia Math. 16 (1989), 46-68. For those with access, this article may be viewed at Science Direct.
  • Butzer, P. L., and R. J. Nessel, Aspects of de La Vallée Poussin’s work in approximation and its influence, Archive Hist. Exact Sciences 46 (1993), 67-95. For those with access, this article may be viewed at SpringerLink.
  • Butzer, P. L., G. Schmeisser, and R. L. Stens, James Gourlay Clunie, 1926-2013. Excerpted from their paper: The classical and approximate sampling theorems and their equivalence for entire functions of exponential type, J. Approx. Theory 179 (2014), 94-111.
  • Butzer, P. L., G. Schmeisser, and R. L. Stens, Qazi Ibadur Rahman, 1934-2013. Excerpted from their paper: The classical and approximate sampling theorems and their equivalence for entire functions of exponential type, J. Approx. Theory 179 (2014), 94-111.
  • Butzer, P. L., M. Schmidt, and E. L. Stark, Observations on the history of central B-splines, Archive Hist. Exact Sciences 39 (1988), 137-156. For those with access, this article may be viewed at SpringerLink
  • Butzer, P. L., and E. L. Stark, The singular integral of Landau alias the Landau polynomials – Placement and impact of Landau’s article “Über die Approximation einer stetigen Funktion durch eine ganze rationale Funktion”, in Edmund Landau, Collected Works, Volume 3, eds. P. T. Bateman, L. Mirsky, H. L. Montgomery, W. Schall, I. J. Schoenberg, W. Schwarz, and H. Wefelscheid, 83-111, Thales-Verlag, Essen.
  • Butzer, P. L., and R. L. Stens, Sampling theory for not necessarily band-limited functions: a historical overview, SIAM Review 34 (1992), 40-53. For those with access, this article may be viewed electronically at SIAM Review and at JSTOR.
  • Cheney, E. W., Introduction to Approximation Theory, McGraw-Hill Book Co., New York, 1966. The notes at the end of this book, pages 224-233, are especially recommended.
  • Cuyt, A., A bibliography of the works of Prof. Dr. H. Werner, J. Comp. and Applied Math. 19 (1987), 3-8. For those with access, this article can be viewed at Science Direct.
  • Daepp, U, Gauthier, P., Gorkin, P., and G. Schmieder, Alice in Switzerland: The Life and Mathematics of Alice Roth, The Mathematical Intelligencer 27 (2005), 41-53. For those with access, this article may be viewed at Springerlink.
  • Deutsch, F., The convexity of Chebyshev sets in Hilbert space, in Topics in Polynomials of One and Several Variables and Their Applications, eds. Th. M. Rassias, H. M. Srivastava, and A.Yanushauskas, World Scientific Publ. Co., 1993, 143-150. A brief historical account of work on the open question of whether every Chebyshev set in a Hilbert space must be convex.
  • Deutsch, F., Best Approximation in Inner Product Spaces, CMS Book in Mathematics, Springer-Verlag, New York, 2001. Each chapter ends with an interesting and useful section of “Historical Notes”.
  • Elliott, D., Lagrange interpolation — decline and fall?, Internat. J. Math. Edu. Sci. Tech. 10 (1979), 1-12.
  • Erdelyi, T., and P. Vértesi, In Memoriam: Paul Erdős (1913-1996), J. Approx. Theory 94 (1998), 1-41. The article also contains a bibliography of Erdős’ work in approximation theory compiled by J. Szabados. For those with access, this article may be viewed at Science Direct.
  • Farouki, R. T., The Bernstein polynomial basis: a centennial retrospective, Comput. Aided Geom. Design 29 (2012), no. 6, 379–419.
  • Garloff, J., A. P. Smith, Preface, in Special Issue on the Use of Bernstein Polynomials in Reliable Computing: A Centennial Anniversary of Reliable Computing 17 (2012), i-vi.
  • Gasca, M., and T. Sauer, On the history of multivariate polynomial interpolation. Numerical analysis 2000, Vol. II: Interpolation and extrapolation, J. Comput. Appl. Math. 122 (2000), 23-35. For those with access, this article may also be viewed at Science Direct.
  • Gautschi, W., A survey of Gauss-Christoffel quadrature formulae, in E. B. Christoffel, The Influence of his Work on Mathematics and the Physical Sciences, eds. P. L. Butzer, F. Feher, 72-147, Birkhäuser, Basel, 1981.
  • Golinskii, L., On the Scientific Legacy of Ya. L. Geronimus, Self-Similar Systems (Dubna, 1998), 273-281, Joint Inst. Nuclear Res., Dubna, 1999. An English translation by the author is here.
  • Goncharov, V. L., The Theory of Best Approximation of Functions, J. Approx. Theory 106 (2000), 2-57. This article, here translated into English, was originally published in 1945 in the collection The Scientific Heritage of P. L. Chebyshev. I. Mathematics, 122-172, Nauka. See also the commentary by V. M. Tikhomirov on pages 58-65 which follows the above article. For those with access, this article may be viewed at Science Direct. The commentary by V. M. Tikhomirov may be viewed atScience Direct.
  • Hsu, L. C., A survey of some recent developments of approximation theory in China, in Approximation Theory, IV (College Station, Tex., 1983), eds. C. K. Chui, L. L. Schumaker and J. D. Ward, 123-151, Academic Press, New York, 1983.
  • Kotlyar, B. D., S. M. Nikolskii, V. G. Ponomarenko, V. M. Tikhomirov, V. N. Trofimov, and P. L. Ulyanov, Aleksandr Filippovich Timan, (Russian) Uspekhi Mat. Nauk 44 (1989), no. 3(267), 145-146; translation in Russian Math. Surveys 44 (1989) no. 3, 179-180. The English translation of this article can be viewed at IOPScience.
  • Lorentz, G. G., Superpositions, metric entropy, complexity of functions, widths, Bull. London Math. Soc. 22 (1990), 64-71. This is one of the articles within a series dedicated to thework of Andrei Nikolaevich Kolmogorov which appeared in Bull. London Math. Soc. 22 (1990), 31-100. See here for the full article.
  • Lorentz, G. G., Mathematics and Politics in the Soviet Union from 1928 to 1953, J. Approx. Theory 116 (2002), 169-223. For those with access, this article may be viewed at Science Direct.
  • Lyubich, Yu. I., Naum Il’ich Akhiezer, (in Russian) Teor. Funktsii Funktsional. Anal. i Prilozhen. 56 (1991), no. 4, 3-14; translation in J. Math. Sci. 76 (1995), no. 4, 2441–2451.
  • Marchenko, V. A., Yu. A. Mitropol’skii, V. A. Pogorelov, A. M. Samoilenko, I. V. Skrypnik, E. Ya. Khruslov, Naum Il’ich Akhiezer (on the centenary of his birth), (in Russian Ukrain. Mat. Zh. 53 (2001), no. 3, 291-293; translation in Ukrainian Math. J. 53 (2001), no. 3, 333–335.
  • Micchelli, C. A., On the work of Theodore J. Rivlin, in “The heritage of P. L. Chebyshev: a Festschrift in honor of the 70th birthday of T. J. Rivlin”, Ann. Numer. Math. 4(1-4) (1997) viii-xiv.
  • Mitrpol’skii, Yu. A., V. K. Dzyadyk, and V. T. Gavrilyuk, Evgen’ii Yakovlevich Remez (on the occasion of the ninetieth anniversary of his birth), (in Russian) Ukrain. Mat. Zh. 38 (1986), 539-540.
  • Nevai, P., Geza Freud, Orthogonal Polynomials and Christoffel Functions (A Case Study), J. Approx. Theory 48 (1986), 3-167. For those with access, this article may be viewed at Science Direct.
  • Nikol’skii, S. M., A.A. Privalov and P.L. Ul’yanov, Pavel Petrovich Korovkin (on his seventieth birthday), Uspekhi Mat. Nauk 39:1 (1984), 179-180; translation in Russian Maths. Surveys 39:1 (1984), 209-211. This article in Russian can be viewed here, and in English (for those with access) here.
  • Nikol’skii, S. M., A.A. Privalov and P.L. Ul’yanov, Pavel Petrovich Korovkin (Obituary), Uspekhi Mat. Nauk 41:5 (1986), 155-156; translation in Russian Maths. Surveys 41:5 (1986), 119-121. This article in Russian can be viewed here, and in English (for those with access) here.

  • Schaback, R., Helmut Werner, a vita written specifically for this website.
  • Schoenberg, I. J., List of Publications, essentially as it appears in I. J. Schoenberg, Selected Papers, ed. C. de Boor, Volume I, pp. xi-xviii, Birkhäuser, Boston, 1988.
  • Sewell, W. E., Remarks on the mathematical researches of J. L. Walsh, SIAM J. Numer. Anal. 3 (1966), 344-348. For those with access, this article may be viewed at SIAM J. Numer. Anal. and at JSTOR.
  • Siegmund-Schultze, R., Der Beweis des Weierstraßschen Approximationssatzes 1885 vor dem Hintergrund der Entwicklung der Fourieranalysis (German) [The proof of Weierstrass’ approximation theorem of 1885 against the background of the development of Fourier analysis], Historia Math. 15 (1988), 299-310. For those with access, this article may be viewed at Science Direct.
  • Stark, E. L., Bernstein-Polynome 1912-1955, Functional Analysis and Approximation (Oberwolfach 1980), Internat. Ser. Numer. Math. 60, Birkhäuser, Basel-Boston, 1981, pp.443-461. Discusses Bernstein’s introduction of Bernstein polynomials in his 2-page paper on Weierstrass’ Theorem and the resulting literature, including the problem of dating Bernstein’s paper.
  • Steffens, K.-G., The History of Approximation Theory From Euler to Bernstein, Birkhäuser, Boston, 2006.
  • Stone, M., A reminiscence on the extension of the Weierstrass approximation theorem, Historia Math. 3 (1976), 328. For those with access, this article may be viewed at Science Direct.
  • Szegö, G., The contribution of L. Fejér to the constructive function theory, in Proceedings of the Conference on Constructive Theory of Functions, eds. G. Alexits and S. B. Stechkin, 19-26, Budapest, 1972.
  • Tikhomirov, V. M., A. N. Kolmogorov and approximation theory, (in Russian) Uspekhi Mat. Nauk 44 (1989), 83-122; translation in Russian Math. Surveys 44 (1989), 101-152.
  • Tikhomirov, V. M., The papers of P. L. Chebyshev on approximation theory, (Russian) Vestnik Moskov. Univ. Ser. I Mat. Mekh. 119 (1995), 86-90; translation in Moscow Univ. Math. Bull. 50 (1996), 39-42.
  • Todd, J., Applications of transformation theory: a legacy from Zolotarev (1847-1878), in Approximation theory and Spline Functions, eds. S. P. Singh, J. H. W. Burry, and B. Watson, 207-245, Reidel, Dordrecht, 1984.
  • Todd, J., A legacy from E. I. Zolotarev (1847-1878), Math. Intelligencer 10 (1988), 50-53.
  • Turán, P., On some open problems of approximation theory, J. Approx. Theory 29 (1980), 23-85. For those with access, this article may be viewed at Science Direct. Pages 86-89, (for those with access here) just following this paper, contain a list of articles dealing with Turán’s Problems as presented in the above paper.
  • Videnskii, V. S., Sergei Natanovich Bernshtein – Founder of the constructive theory of functions. Uspehi Mat. Nauk 16 1961 no. 2 (98), 21–24. In English in Russian Math. Surveys 16 1961, 17-20. See here.
  • Vinogradov, O. L., V. V. Zhuk, V. L. Fainshmidt, and V. P. Khavin, Garal’d Isidorovich Natanson, Proceedings of the St. Petersburg Mathematical Society, X (2005), 237–252, also appears in Amer. Math. Soc. Transl. Ser. 2, 214, Amer. Math. Soc., Providence, RI, 2005.
  • Vlasov, V. F., A. N. Kolmogorov, V. G. Ponomarenko, V. N. Trofimov, and B. D. Judin, Aleksandr Filippovic Timan (on the occasion of his sixtieth birthday). (Russian) Uspekhi Mat. Nauk 36 (1981), no. 2(218), 221-226.
  • Vulih, B. Z., M. K. Gavurin, and S. M. Lozinskii, Isidor Pavlovic Natanson. Obituary. (in Russian) Uspehi Mat. Nauk 20 (1965), no. 1 (121), 171-175. In English (for those with access).
  • Werner, I., In Memoriam, pages VII-IX of Rational Approximation and its Applications in Mathematics and Physics, (Lancut, 1985), 331–350, LNM 1237, Springer, Berlin, 1987.
  • Widder, D. V., Joseph Leonard Walsh, SIAM J. Numer. Anal. 3 (1966), 171-172. For those with access, this article may be viewed electronically at SIAM J. Numer. Anal. and at JSTOR.
  • Wynn, P., The work of E. B. Christoffel on the theory of continued fractions, in E. B. Christoffel, The Influence of his Work on Mathematics and the Physical Sciences, eds. P. L. Butzer, F. Feher, 190-202, Birkhäuser, Basel, 1981.

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