ὅδε οἶκος, ὦ ἑταῖρε, μνημεῖον ἐστιν ζῴων τῶν σοφῶν ἀνδρῶν, καὶ τῶν ἔργων αὐτῶν
R. Bojanic

RANKO BOJANIĆ

(1925 - 2017)

Ranko Bojanić was Professor Emeritus at The Ohio State University best known for his achievements in the field of Approximation Theory.

Ranko Bojanić, the son of Gojko and Jelena Bojanić, was born on November 12, 1924 in The Kingdom of Yugoslavia. He was raised in Belgrade, where he attended The Male Gymnasium of King Aleksandar I. After the WWII, he entered The University of Belgrade, studying at Faculty of Natural Sciences and Mathematics. In 1950, he was elected to the position of Assistant at the Mathematical Institute of Serbian Academy of Sciences, where he spent three years working on his doctoral dissertation under the supervision of his Advisor, Prof. Jovan Karamata. In 1953 he successfully defended his thesis "Propriétés Aymptotiques des Solutions des Équations Différentielles Lineaires" at the Serbian Academy of Sciences. In the same year, he was awarded a scholarship by the Federal Commission for Cultural Relations with Foreign Countries, and he moved to Switzerland to carry on his work. In the period between 1954 and 1958, he was engaged as a Research Associate at the Mathematical Institute, which he represented at the Fourth Austrian Mathematics Congress in Vienna (1956). In 1958 he was elected a Research Associate at the Tata Institute Fundamental Research in Bombay (India), and in 1959 he was invited as Lecturer at the Stanford University. Apart from three years as Assistant Professor at the University of Notre Dame in Indiana (1960 - 1963), the largest part of his career was spent at the Ohio State University (1963 - 1995). He collaborated successfully with colleagues around the world, and his most fruitful work was conducted with his friend and colleague from both the Mathematical Institute and Ohio State University, the late Prof. Bogdan Bajsanski.


List of Publications
  1. Ball, S., & Bojanic, R. (2000). Table Look-Up Method for the Evaluation of Functions. Journal of Approximation Theory,107(1), 160-162. doi:10.1006/jath.2000.3489
  2. Bojanic, R., Della Vecchia, B., & Mastroianni, G. (1999). On the Approximation of Bounded Functions with Discontinuities of the First Kind by Generalized Shepard Operators. Acta Mathematica Hungarica,85(1), 29-57. doi:10.1023/A:1006612727274
  3. Humphreys, N., & Bojanic, R. (1999). Rate of convergence for the absolutely (C,a) summable Fourier series of functions of bounded variation. J. Approx. Theory,101(2), 212-220.
  4. Bojanic, R., & Tomic, M. (1995). Slobodan Aljančić (1922-1993). Publications de l Institut Mathematique,(N.S.)58(72), 7-12. Retrieved March 21, 2017, from http://elib.mi.sanu.ac.rs/files/journals/publ/78/n072p007.pdf.
  5. Bojanic, R., & Cheng, F. (1992). Estimates for the rate of approximation of functions of bounded variation by Hermite-Fejér polynomials. Acta Mathematica Hungarica,59(1-2), 91-102.
  6. Bojanic, R., & Cheng, F. (1992). Rate of convergence of Hermite-Fejér polynomials for functions with derivatives of bounded variation. Acta Mathematica Hungarica,59(1), 91-102. doi:10.1007/BF00052094
  7. Kazik Kahn, M., & Bojanic, R. (1992). Summability of Hermite-Fejér interpolation for functions of bounded variation. Journal of Natural Sciences and Mathematics,32(1), 5-10.
  8. Mitrovic, S., Bojanic, R. (1992). An algorithm for the approximation by cubic splines. Mat. Vesnik,44(3-4), 123–126.
  9. Bojanic, R., & Kazim Khan, M. (1991). Rate of convergence of some operators of functions with derivatives of bounded variation. Atti del Seminario Matematico e Fisico dell'Università di Modena,39, 495-512.
  10. Baishanski, B., & Bojanic, R. (1990). λ-regular oscillation and applications. Publications de l Institut Mathematique,(N.S.)48(62), 73-82. Retrieved March 21, 2017, from http://elib.mi.sanu.ac.rs/files/journals/publ/68/9.pdf.
  11. Bojanic, R., & Cheng, F. (1989). Rate of convergence of Bernstein polynomials for functions with derivatives of bounded variation. Journal of Mathematical Analysis and Applications,141(1), 136-151. doi:https://doi.org/10.1016/0022-247X(89)90211-4.
  12. Bojanic, R., & Divis, Z. (1988). Asymptotic behaviour of partial sums of Fourier-Legendre series. Publications de l Institut Mathematique,(N.S.)44(58), 49-64. Retrieved March 21, 2017, from http://elib.mi.sanu.ac.rs/files/journals/publ/64/n058p049.pdf.
  13. Baishanski, B., & Bojanic, R. (1986). An estimate for the coefficients of polynomials of given length. Journal of Approximation Theory,48(2), 181-188. doi:10.1016/0021-9045(86)90002-X
  14. Bojanic, R., & Divis, Z. (1984). An Estimate for the Rate of Convergence of the Eigenfunction Expansions of Functions of Bounded Variation. Applicable Analysis,17(3), 227-242. doi:10.1080/00036818408839498
  15. Bojanic, R., & Stanojevic, C. V. (1982). A Class of L 1 -Convergence. Transactions of the American Mathematical Society,269(2), 677-683. doi:10.2307/1998474
  16. Bojanic, R., & Vuilleumier, M. (1981). On the rate of convergence of Fourier-Legendre series of functions of bounded variation. Journal of Approximation Theory,31(1), 67-79. doi:10.1016/0021-9045(81)90031-9
  17. Bojanic, R. (1980). Necessary and sufficient conditions for the convergence of the extended Hermite-Fejér interpolation process. Acta Mathematica Academiae Scientiarum Hungaricae,36(3), 271-279. doi:10.1007/BF01898143
  18. Bojanic, R. (1979). An estimate of the rate of convergence for Fourier series of functions of bounded variation. Publications de l Institut Mathematique,(N.S.)26(40), 57-60. Retrieved March 23, 2017, from http://elib.mi.sanu.ac.rs/files/journals/publ/46/8.pdf.
  19. Bojanic, R., Prasad, J., & Saxena, R. B. (1979). An upper bound for the rate of convergence of the Hermite-Fejér process on the extended Chebyshev nodes of the second kind. Journal of Approximation Theory,26(3), 195-203. doi:10.1016/0021-9045(79)90057-1
  20. Bojanic, R. (1975). Bernstein's Constant And Best Approximatioin On [0, ∞). Publications de l Institut Mathematique,(N.S.)18(32), 19-30. Retrieved March 21, 2017, from http://elib.mi.sanu.ac.rs/files/journals/publ/38/2.pdf.
  21. Bojanic, R. (1975). Degree of L1 approximation to integrable functions by modified Bernstein polynomials. Journal of Approximation Theory,13(1), 66-72. doi:10.1016/0021-9045(75)90015-5
  22. Bojanic, R., & Ahlswede, R. (1975). Approximation o continuous functions in p-Adic Analysis. Journal of Approoximation Theory,15(3), 190-205.
  23. Bojanic, R. (1974). A simple proof of Mahler's theorem on approximation of continuous functions of a p-adic variable by polynomials. Journal of Number Theory,6(6), 412-415. doi:10.1016/0022-314X(74)90038-9
  24. Bojanic, R. (1974). Approximation of continuous, periodic functions by discrete linear positive operators. Journal of Approximation Theory,11(3), 231-235. doi:10.1016/0021-9045(74)90015-X
  25. Bojanic, R., & Elkins, J.M. (1974). Bernstein's constant and best approximation on ...0, ...). Publications de l'Institut Mathématique,32, 19-30.
  26. Bojanic, R., & Roulier, J. (1974). Approximation of convex functions by convex splines and convexity preserving continuous linear operators. Journal of Numerical Analysis and Approximation Theory,3(2), 143-150.
  27. Bojanic, R., & Lee, Y. H. (1974). An Estimate for the Rate of Convergence of Convolution Products of Sequences. SIAM Journal on Mathematical Analysis,5(3), 452-462. doi:10.1137/0505046
  28. Bojanic, R., & Lee, Y. H. (1973). A survey of recent results and problems in the study of convolution products of sequences. In G. G. Lorentz (Ed.), Approximation Theory (pp. 263-269). New York: London: Academic Press Inc.
  29. Bojanic, R., & Shisha, O. (1973). On the precision of uniform approximation of continuous functions by certain linear positive operators of convolution type. Journal of Approximation Theory,8(2), 101-113. doi:10.1016/0021-9045(73)90019-1
  30. Bojanic, R., & Seneta, E. (1973). A unified theory of regularly varying sequences. Mathematische Zeitschrift,134(2), 91-106. doi:10.1007/BF01214468
  31. Bojanic, R., & Vuilleumier, M. (1973). Asymptotic properties of linear operators. L'Enseignement Mathématique,283-309. doi:10.5169/seals-46293
  32. Bojanic, R. (1972). A note on the precision of interpolation by Hermite-Fejer polynomials. In Proceedings, Conference on Constructive Theory of Functions (pp. 69-76). Budapest: Akademiaikiado.
  33. Bojanic, R., & Seneta, E. (1971). Slowly varying functions and asymptotic relations. Journal of Mathematical Analysis and Applications,34(2), 302-315. doi:10.1016/0022-247X(71)90114-4
  34. Bojanic, R. (1969). A note on the degree of approximation to continuous functions. L'Enseignement Mathématique,15(1), 43-53. doi:10.5169/seals-43203
  35. Bojanic, R., & De Vore, R. (1969). A proof of Jackson's theorem. Bulletin of the American Mathematical Society,75, 364-367. doi:10.1090/S0002-9904-1969-12174-9
  36. Bojanic, R., & Karamata, J. (1967). A convergence test for Fourier series. Indian Journal of Mathematics, 9.
  37. Bojanic, R., Gould, H. W., Lansing, D. L., . . . Amos, D. E. (1967). A Finite Series (J. P. Church). SIAM Review,9(4), 749-750. doi:10.1137/1009125
  38. Bojanic, R., & De Vore, R. (1966). On Polynomials of Best One-Sided Approximation. L'Enseignement Mathématique,12, 139-164.
  39. Bojanic, R. (1965). A Complement to Cauchy's Theorem. The American Mathematical Monthly,72(3), 297-300. doi: 10.2307/2313706
  40. Bojanic, R. (1965). An Asymptotic Result on a Zero of a Function (R. L. Graham and L. Shepp). SIAM Rievew,7(2), 280-283. Retrieved March 22, 2017, from http://www.jstor.org/stable/2027280.
  41. Bajsanski, B., & Bojanic, R. (1964). A note on approximation by Bernstein polynomials. Bulletin of the American Mathematical Society,70, 675-677. doi:10.1090/S0002-9904-1964-11156-3
  42. Bateman, P. T., Rubel, L. A., Koh, K., Potter, J. E., Fitzgerald, R., Bojanic, R., . . . Livingston, A. E. (1964). Problems for Solution: 5171-5180. The American Mathematical Monthly,71(2), 215-217. doi:10.2307/2311772
  43. Bojanic, R., & Musielak, J. (1964). An Inequality for Functions with Derivatives in an Orlicz Space. Proceedings of the American Mathematical Society,15(6), 902-906. doi: 10.2307/2034906
  44. Bergman, S., & Bojanic, R. (1962). Application of integral operators to the theory of partial differential equations with singular coefficients. Archive for Rational Mechanics and Analysis,10, 323-340.
  45. Bojanic, R., & Stoll, W. (1962). A Characterization of Monomials. Proceedings of the American Mathematical Society,16(1). doi:10.2307/2033784
  46. Bojanic, R. (1961). Slowly oscillating functions and their applications. Math. Student,27(1959), 117-128.
  47. Bergman, S., Bojanic, R. (1961). On some relations between integral operators. Scripta Math.,25, 317-321.
  48. Bojanic, R. (1959). On the approximation of continuous functions by Bernstein polynomials. Bulletin de l'Académie Serbe des Sciences et des Arts,232, 59-65. [In Serbian]
  49. Bojanic, R. (1958). Sur l'approximation des fonctions continues par les polynômes de Bernstein. Glas Srpske Akad. Nauka 232 Od. Prirod.-Mat. Nauka,(N.S.)15, 59-65. [In Serbo-Croatian]
  50. Aljancic, S., Bojanic, R. & Tomic, M. (1956). Sur Le Comportement Asymptotique Au Voisinage De Zéro Des Séries Trigonométriques De Sinus À Coefficients Monotones. Publications de l Institut Mathematique,(S.S.)X(10), 101-120. Retrieved March 21, 2017, from http://elib.mi.sanu.ac.rs/files/journals/publ/16/11.pdf.
  51. Bojanic, R. (1956). On Uniform Convergence Of Fourier Series. Publications de l Institut Mathematique,(S.S.)X(10), 153-158. Retrieved March 21, 2017, from http://elib.mi.sanu.ac.rs/files/journals/publ/16/14.pdf.
  52. Bojanic, R., Jurkat, W., & Peyerimhoff, A. (1956). Über einen Taubersatz für Faltungen. Math. Z.,65, 195-199. [In German]
  53. Aljancic, S., Bojanic, R., & Tomic, M. (1955). Sur L'Intégrabilité De Certaines Séries Trigonométriques. Publications de l Institut Mathematique,(S.S)8(8), 67-84. Retrieved March 21, 2017, from http://elib.mi.sanu.ac.rs/files/journals/publ/14/8.pdf. [In French]
  54. Aljancic, S., Bojanic, R., & Tomic, M. (1955). Deux Théorèmes Relatifs au Comportement Asymptotique des Séries Trigonométriques. Zbornik Radova. Matematicki institut,4, 15-26. Retrieved March 28, 2017, from http://elib.mi.sanu.ac.rs/files/journals/zr/4/n004p015.pdf. [In Serbian]
  55. Bojanic, R. (1955). Remarque sur un procédé de formation des équations aux dérivées partielles. Fac. Philos. Uni. Skopje. Sect. Sci. Nat. Annuaire,8, 71–73. [In Serbo-Croatian]
  56. Bojanic, R. (1955). Quelques problèmes de sommation. Bull. Soc. Math. Phys. Macédoine,6, 9-17. [In Serbo-Croatian]
  57. Erdos, P., & Bojanic, R. (1955). Advanced Problems and Solutions: Solutions: 4590. Amer. Math. Monthly,62(7), 498-499.
  58. Aljancic, S., Bojanic, R., & Tomic, M. (1954). Sur La Valeur Asymptotique D'Une Classe Des Intégrales Définies. Publications de l Institut Mathematique,(S.S)7(7), 81-94. Retrieved March 21, 2017, from http://elib.mi.sanu.ac.rs/files/journals/publ/13/6.pdf. [In French]
  59. Bajšanski, B. & Bojanic, R. (1954). On two sums. Bull. Soc. Math. Phys. Macédoine,5, 34-36. [In Serbo-Croatian]
  60. Bojanic, R., & Tomic, M. (1954). Sur L'Ordre De Grandeur De La Transformée De Sinus De Fourier. Publications de l Institut Mathematique,(S.S)7(7), 41-46. Retrieved March 21, 2017, from http://elib.mi.sanu.ac.rs/files/journals/publ/13/2.pdf. [In French]
  61. Bojanic, R. (1954). L'évaluation asymptotique de la somme de diviseurs des certains nombres. Bull. Soc. Math. Phys. Macédoine,5, 5–15. [In Serbo-Croatian]
  62. Erdos, P., & Bojanic, R. (1953). Advanced Problems and Solutions: Solutions: 4487. Amer. Math. Monthly,60(6), 428–429.
  63. Bojanic, R., & Vuckovic V. (1953). Über die Eigenfunktionen der Schwingenden Platte. Zbornik radova. Matematički institut,3, 107-128. Retrieved March 28, 2017, from http://elib.mi.sanu.ac.rs/files/journals/zr/3/n003p107.pdf. [In Serbian]
  64. Bojanic, R. (1953). Propriétés Aymptotiques des Solutions des Équations Différentielles Lineaires. Zbornik radova. Matematicki institut,3, 213-254. Retrieved March 28, 2017, from http://elib.mi.sanu.ac.rs/files/journals/zr/3/n003p213.pdf. [In Serbian]
  65. Bojanic, R. (1952). Über die Konvergenz Einer Folge von Polynomen. Zbornik radova. Matematički institut,2, 133-136. Retrieved March 28, 2017, from http://elib.mi.sanu.ac.rs/files/journals/zr/2/n002p133.pdf. [In Serbian]
  66. Bojanic, R. (1952). Ein Existenzastz Über die Lösungen einer Klasse Impliziter Differentialgleichungen Erster Ordnung. Zbornik radova. Matematički institut,2, 137-142. Retrieved March 28, 2017, from http://elib.mi.sanu.ac.rs/files/journals/zr/2/n002p137.pdf. [In Serbian]
  67. Bojanic, R. (1950). Sur la formule des accroissements finis. Publications de l Institut Mathematique,(S.S)3(1), 219-226. Retrieved March 21, 2017, from http://elib.mi.sanu.ac.rs/files/journals/publ/9/17.pdf. [In French]
  68. Bojanic, R. (1950). On the first mean-value theorem. Glas Srpske Akad. Nauka. Od. Prirod.-Mat. Nauka,198, 187–196. [In Serbo-Croatian]
  69. Bojanic, R. (1949). Une propriété caractéristique des courbes du second degré. Bull. Soc. Math. Phys. Serbie,1(3-4), 105–111. [In Serbian]
  70. Bojanić, R. (1949). Jedna karakteristična osobina koničnih preseka. Matematički Vesnik,3, 105-111. [In Serbian]

References
  1. Godišnjak Srpske akademije nauka (Vol. LVII, p. 19). (1950). Belgrade: Srpska akademija nauka.
  2. Godišnjak Srpske akademije nauka (Vol. LX, p. 173). (1953). Belgrade: Srpska akademija nauka.
  3. Godišnjak Srpske akademije nauka (Vol. LXIII, p. 101). (1959). Belgrade: Srpska akademija nauka.
  4. Godišnjak Srpske akademije nauka (Vol. LXV, p. 139). (1959). Belgrade: Srpska akademija nauka.
  5. Godišnjak Srpske akademije nauka (Vol. LXVI, p. 114). (1960). Belgrade: Srpska akademija nauka.
  6. Hailpern, R. (Ed.). (1963). News and Notices. The American Mathematical Monthly,70(9), 1034. Retrieved March 7, 2017, from http://www.jstor.org/stable/2313105.
  7. Ranko Bojanic Obituary. (2017, February 25). Retrieved March 7, 2017, from http://www.legacy.com/obituaries/dispatch/obituary.aspx?pid=184243052.
  8. Student Directory of the University of Notre Dame 1960 - 1961(p. 6). (1961). Retrieved March 7, 2017, from http://archives.nd.edu/dir/DIR_1960_1961.pdf.
  9. Zapisnik 55. sednice Naučnog saveta Matematičkog instituta SAN (Rep.). (June 16, 1953). [Unpublished]


Author:
Šegan-Radonjić, Marija
30.05.2017.