Christian Berg's personal homepage

A short CV


Since 1.9.2014 I am Professor emeritus

Retirement lecture September 26, 2014 (In Danish)

Teaching in the academic year 2013-2014

Teaching in the academic year 2012-2013

Teaching in the academic year 2011-2012

Teaching in previous years can be found at the bottom of the page.

Research activities

My research is supported by a Grant from FNU (The Danish Council for Independent Research | Natural Sciences) "Complex Methods in Dynamical Systems and Special Functions" for the years 2011-2013 (continuing a 2008-2010 grant). It is shared with Professor Henrik Laurberg Pedersen (KU-LIFE), Associate Professor Carsten Lunde Petersen (RUC) and Associate Professor Christian Henriksen (DTU). I am member of the steering committee for a NordForsk Grant for the years 2009-2011 headed by Irina Markina, University of Bergen.

Conferences organized

  • "Workshop on Orthogonal Polynomials,Hankel and Jacobi matrices", August 26-28, 2009, Copenhagen.
  • "Workshop on Integral Transforms Positivity and Applications" , September 1-3, 2010, Copenhagen.
  • "International Symposium on Orthogonal Polynomials and Special Functions - a Complex Analytic Perspective", Copenhagen, June 11-June 15, 2012.
  • "Workshop on Special Functions and their Applictions", Copenhagen, August 28-30, 2013.

    Recent publications and manuscripts

  • 132: With R. Szwarc, Indeterminate Jacobi operators. Journal of Operator Theory (to appear) pdf-version from ArXiv .
  • 131: With R. Szwarc, Self-adjoint operators associated with Hankel moment matrices. Journal of Functional Analysis 283 (2022) 109674 access via DOI pdf-version from ArXiv .
  • 130: With Jacob S. Christiansen, The Moment Problem, pages 269-306 In: Encyclopedia of Special Functions. The Askey-Bateman Project Volume I. Univariate Orthogonal Polynomials. Editor Mourad E. H. Ismail. Cambridge University Press, Cambridge UK 2020.
  • 129: With Henrik L. Pedersen, A family of Horn-Bernstein functions. Experimental Mathematics access via DOI pdf-version from ArXiv.
  • 128: With A. Cetinkaya and D. Karp, Completely monotonic ratios of basic and ordinary gamma functions. Aequationes Mathematicae 95 (2021), 569-588 access via DOI , pdf-version from ArXiv
  • 127: A unified view of space-time covariance functions through Gelfand pairs. J. Fourier Anal. Appl. 26 (2020), pdf-version from ArXiv, access via DOI ,
  • 126: With R. Szwarc, Closable Hankel operators and moment problems. Integr. Equ. Oper. Theory 92, issue 1 (2020), access via DOI , pdf-version from ArXiv.
  • 125: With S. Koumandos and Henrik L. Pedersen, Nielsen's beta function and some infinitely divisible distributions. Math. Nachrichten 294 (2021) pdf-version from ArXiv, access via DOI
  • 124: With Ana P. Peron and Eugenio Massa, A family of entire functions connecting the Bessel function J_1 and the Lambert W function. Constructive Approximation 53 (2021), 121-154 access via DOI , pdf-version from ArXiv,
  • 123: A two parameter extension of Urbanik's product convolution semigroup. Probability and Mathematical Statistics 39(2) (2019), 441-458 access via DOI
  • 122: With R. Szwarc, Inverse of infinite Hankel moment matrices. SIGMA 14 no 109 (2018), 48 pages access via DOI
  • 121: With Ana P. Peron and E. Porcu, Schoenberg's theorem for real and complex Hilbert spheres revisited. J. Approx. Theory 228 (2018), 58-78 access via DOI
  • 120: With Ana P. Peron and E. Porcu, Orthogonal expansions related to compact Gelfand pairs. Expo. Math. 36 (2018), 259-277 access via DOI
  • 119: With A. Bakan, Solvability of the Hankel determinant problem for real sequences. Chapter 5 in Frontiers in Orthogonal Polynomials and q-Series. Edited by M. Zuhair Nashed and Xin Li (University of Central Florida, USA) World Scientific Publishing Co. Pte. Ltd. Singapore 2018
  • 118: On a family of functions studied by Bhatia and Jain. Experimental Mathematics 26(2) (2017), 241-246 access via DOI
  • 117: With R. Szwarc, Symmetric moment problems and a conjecture of Valent. Sbornik: Mathematics 208:3 (2017), 335-359 DOI:10.1070/SM8732. Russian version: Mat. Sbornik 208:3 (2017), 28-53, DOI:10.4213/sm8732
  • 116: With E. Porcu, From Schoenberg coefficients to Schoenberg functions. Constr. Approx. 45(2) (2017), 217-241 pdf-version from ArXiv, access via DOI
  • 115: With Ryszard Szwarc, A determinant characterization of moment sequences with finitely many mass points. preprint-version Linear and Multilinear Algebra 63 (8) (2015), 1568-1576. access via DOI
  • 114: Asymptotic behaviour of the Urbanik semigroup. preprint-version J. Approx. Theory 195 (2015), 109-121 access via DOI
  • 113: With Ryszard Szwarc, On the order of indeterminate moment problems Adv. Math. 250 (2014), 105-143. final pdf-version access via DOI
  • 112: With Feng Qi, Complete monotonicity of a difference between the exponential function and trigamma functions and properties related to a modified Bessel function Mediterr. j. Math. 10 (2013) no. 4, 1685-1696. final pdf-version access vis DOI
  • 111: With Helle Bjerg Petersen, On an iteration leading to a q-analogue of the Digamma function J. Fourier Anal. Appl. 19,4 (2013), 762-776. access via DOI. final preprint pdf-version
  • 110: With Henrik L. Pedersen, A completely monotonic function used in an inequality of Alzer Computational Methods and Function Theory vol. 12 (2012), 329-341.
  • 109: With Jacob Stordal Christiansen, A question by Chihara about shell polynomials and indeterminate moment problems J. Approx. Theory 163 (2011), 1449-1464 pdf-version from ArXiv access vis DOI
  • 108: With Christophe Vignat, Derivation of an integral of Boros and Moll via convolution of Student t-densities Ramanujan Journal 27 (2012), 147-150 pdf-version from ArXiv access via DOI
  • 107: With Henrik L. Pedersen, A one-parameter family of Pick functions defined by the Gamma function and related to the volume of the unit ball in n-space pdf-version from ArXiv Proc. Amer. Math. Soc. 139 (2011), 2121-2132. access via DOI
  • 106: With Maryam Beygmohammadi, On a fixed point in the metric space of normalized Hausdorff moment sequences Rend. Circ. Mat. Palermo, Serie II, Suppl. 82 (2010), 251-257. preprint version
  • 105: With Ryszard Szwarc, The smallest eigenvalue of Hankel matrices pdf-version from ArXiv Constr. Approx. 34 (2011), 107-133. access via DOI
  • 104: With Christophe Vignat, On the density of the sum of two independent Student t-random vectors pdf-version from ArXiv Statistics and Probability Letters 80 (2010), 1043-1055. access via DOI
  • Biographical Note B{\o}rge Jessen, 19.6.1907--20.3.1993 Electronic journal for History of Probability and Statistics, Vol 5, no. 1 (2009) Access
  • 103: With Antonio J. Dur{\'a}n, Fibonacci numbers, Euler's 2-periodic continued fractions and moment sequences The Fibonacci Quarterly 49 (2011), 66-75. pdf-version from ArXiv
  • 102: With Christophe Vignat, On some results of Cufaro Petroni about Student t-processes J. Phys. A: Math. Theor. 41(2008) 265004 (10 PP) pdf-version from ArXiv access via DOI
  • 101: With Antonio J. Dur{\'a}n, Iteration of the rational function z-1/z and a Hausdorff moment sequence Expo. Math. 26 (2008), 375-385. final pdf-version access via DOI
  • 100: With Ryszard Szwarc, Bounds on Tur{\'a}n determinants J. Approx. Theory 161 (2009), 127-141. pdf-file of preprint version. access via DOI
  • 99: With Jorge Mateu and Emilio Porcu, The Dagum family of isotropic correlation functions Preprint submitted to ArXiv. Bernoulli Journal 14 no. 4 (2008), 1134-1149. access via DOI
  • 98: With J{\o}rgen Ellegaard Andersen, Quantum Hilbert matrices and orthogonal polynomials J. Comput. Appl. Math. 233 (2009), 723-729. Updated preprint version pdf.file. access via DOI
  • Expository writing: Ortogonale polynomier og Hilbertmatricen (In Danish) NORMAT 54 no. 3 (2006) 116-133. pdf-file. (Note that the page numbers in the pdf-file are not the final numbers as they appeared in the journal)
  • 97: With Henrik L. Pedersen, Convexity of the median in the gamma distribution Ark. Mat. 46 (2008), 1-6. pdf-file.
  • 96: Stieltjes-Pick-Bernstein-Schoenberg and their connection to complete monotonicity. In: Positive definite functions. From Schoenberg to Space-Time Challenges. Ed. J. Mateu and E. Porcu. Dept. of Mathematics, University Jaume I, Castellon, Spain, 2008. ISBN 978-84-612-8282-1. pdf-file.
  • 95: Fibonacci numbers and orthogonal polynomials Arab J. Math. Sci. 17 (2011), 75-88. Submitted version , access via DOI (Originally to appear in proceedings of an International Conference on Mathematical Analysis and Its Applications, Assiut, Egypt, January 3-6, 2006, but this never happened.) pdf-version submitted September 2006 to ArXiv. The Arxiv-link contains an updated version from August 5, 2010.
  • 94: With Antonio Duran, The fixed point for a transformation of Hausdorff moment sequences and iteration of a rational function Math. Scand. 103 (2008), 11-39. pdf-file .
  • 93: With Henrik L. Pedersen and with an appendix by Walter Hayman Logarithmic order and type of indeterminate moment problems Proceedings of the International Conference : "Difference equations, special functions and orthogonal polynomials", Munich, July 25-30, 2005. World Scientific Publishing Company, Singapore 2007 (ISBN-13 978-981-270-643-0; ISBN-10 981-270-643-7). Editors: S.Elaydi, J. Cushing, R. Lasser, V. Papageorgiou, A. Ruffing, W. Van Assche. pdf-file.
  • 92: With Christophe Vignat, Linearization coefficients of Bessel polynomials Constr. Approx. Vol. 27 (2008),15-32. pdf-file. access via DOI
  • 91: On powers of Stieltjes moment sequences,II J. Comput. Appl. Math. 199 (2007), 23-38. pdf-file. access via DOI
  • 90: With Henrik L. Pedersen, The Chen-Rubin conjecture in a continuous setting Manuscript containing Maple programs pdf-file. Revised manuscript of August 24, 2006 has appeared in Methods and Applications of Analysis, Vol 13 (2006), 63-88. revised version (pdf).
  • 89: Integral representation of some functions related to the Gamma function, Mediterr. j. math. 1 (2004), 433-439. Birkh{\"a}user pdf-file of preprint version.
  • 88: With Horst Alzer and Stamatis Koumandos, On a conjecture of Clark and Ismail J. Approx. Theory 134 (2005), 102-113. ps-file of preprint version.
  • 87: With Antonio Duran, Some transformations of Hausdorff moment sequences and harmonic numbers Canad. J. Math. 57 (2005), 941-960. ps-file of Preprint version.
  • 86: On powers of Stieltjes moment sequences,I J. Theor. Prob. 18 (2005), 871-889. Preprint version pdf-file.
  • 85: With Horst Alzer, Some Classes of Completely Monotonic Functions,II Ramanujan J. 11 (2006), 225-248. Journal version Preprint version: pdf-file.
  • 84: On a generalized Gamma convolution related to the q-calculus In: Developments of Mathematics Vol. 13: "Theory and Applications of Special Functions. A volume dedicated to Mizan Rahman". Edited by Mourad E.H. Ismail and Erik Koelink. ISBN: 0-387-24231-7. Springer Science+Business Media, Inc., Berlin. A preprint version of the paper is available: pdf-file.
  • 83: With Antonio Duran, Orthogonal polynomials and analytic functions associated to positive definite matrices J. Math. Anal. Appl. 315 (2006), 54-67 pdf-file.
  • 82: With Antonio J. Duran, A transformation from Hausdorff to Stieltjes moment sequences Ark. Mat. 42 (2004), 239-257. See: preprint Version of May 2004. pdf-file.
  • 81: Correction to a paper by A. G. Pakes J. Austral. Math. Soc. 76 (2004), 67-73. See pdf-file of preprint.
  • 80: With Horst Alzer, Some Classes of Completely Monotonic Functions Ann. Acad. Sci. Fenn. Math. Vol. 27 (2002), 445-460 pdf-file.
  • 79: A Pick function related to an inequality for the entropy function . J. Inequalities Pure and Appl. Math. Vol. 2, Issue 2, Article 26, 2001. ( Copyright University of Victoria print-version. monitor-version.
  • 78: With H. L. Pedersen, Pick functions related to the Gamma function. Rocky Mountain Journal of Math. 32 no. 2, 507-525 (2002) pdf-file.
  • 77: On infinitely divisible solutions to indeterminate moment problems. In: Proceedings of the International Workshop "Special Functions", Hong Kong, June 21-25, 1999. Ed. C. Dunkl, M. Ismail, R. Wong. World Scientific, Singapore 2000, pp. 31-41. pdf-file. dvi-file.
  • 76: With H. L. Pedersen, A completely monotone function related to the Gamma function. J. Comput. Appl. Math., Vol. 133 (2001), 219-230. ps-file. dvi-file. pdf-file.
  • 75: With A. Ruffing, Generalized q-Hermite Polynomials. Commun. Math. Phys. 223,1 (2001), 29-46 paper.
  • 74: With Y. Chen and M.E.H. Ismail, Small eigenvalues of large Hankel matrices: The indeterminate case. Math. Scand., Vol. 91 (2002), 67-81 pdf-file.
  • 73: From discrete to absolutely continuous solutions of indeterminate moment problems. Arab. J. Math. Sc. 4, no.2 (1998), 1-18. ps-file. dvi-file.
  • 72: On some indeterminate moment problems for measures on a geometric progression. J. Comput. Appl. Math.99 (1998), 67-75. J. Comput. Appl. Math.. ps-file. dvi-file.
  • 71: Moment problems and polynomial approximation, Ann. Fac. Sci. Toulouse Math\'ematiques, 1996, 9-32. Num\'ero sp\'ecial Stieltjes. ps-file. dvi-file.
  • 70: With A.J. Duran, Measures with finite index of determinacy or a mathematical model for Dr. Jekyll and Mr. Hyde, Proc. Amer. Math. Soc. 125 (1997), 523-530. ps-file. dvi-file.
  • 69: Recent results about moment problems, In: Probability Measures on Groups and Related Structures, XI Proceedings Oberwolfach 1994. Ed. H. Heyer, World Scientific, Singapore 1995. ps-file. dvi-file.
  • 67: With A.J. Duran, Orthogonal polynomials, $L^2$-spaces and entire functions , Math. Scand.79 (1996), 209-223. pdf-file. dvi-file.
  • 65: With M.E.H. Ismail, Q-Hermite polynomials and classical orthogonal polynomials, Can. J. Math. 48 (1996), 43-63. ps-file. dvi-file. pdf-file.
  • 56: Markov's theorem revisited. J. Approx. Theory 78 (1994), 260-275. preprint version.
  • 18: Potential theory on the infinite dimensional torus. Inventiones Math. 32 (1976), 49-100. (A note in C.R. Acad. Sci., Paris, 280 (1975), 1519-1521 contains a summary of this paper). scanned version
  • 16: On the support of the measures in a symmetric cocnvolution semigroup. Math. Zeitschrift 148 (1976), 141-146. scanned version
  • 15: With J. Faraut, Semi-groupes de Feller invariants sur les espaces homog\`enes non moyennables Math. Zeitschrift 136 (1974), 279-290 (A note in C.R. Acad. Sci., Paris, vol. 277 (1973), 807-808 contains a summary of this paper). scanned version
  • 14: With J.P. R. Christensen, Sur la norme des op{\'e}rateurs de convolution Inventiones Math. 23 (1974), 173-178. scanned version
  • 11: With G. Forst, Non-symmetric translation invariant Dirichlet forms. Inventiones Math. 21 (1973), 199-212. scanned version
  • 6: Dirichlet forms on symmetric spaces. Ann. Inst. Fourier, Grenoble 23,1 (1973), 135-156. scanned version
  • 4: Suites definies n\'egatives et espaces de Dirichlet sur la sph\`ere S\'eminaire Th\'eorie du Potentiel, Paris, Annee 1969/70. 18pp. scanned version (Two notes in C.R. Acad. Sci. Paris, vol. 271, 488-490, 778-780 contain a summary of this paper). For these see scanned version and scanned version
  • 3: Abstract Steiner points for convex polytopes J. London Math. Soc.(2) 4 (1971), 176-180. scanned version
  • 2: Shephard's approximation theorem for convex bodies and the Milman theorem Math. Scand. 25 (1969), 19-24. scanned version
  • 1: Corps convexes et potentiels sph\'eriques. Mat.-Fys. Medd. Kgl. Danske Vid. Selsk. 37 No. 6 (1969), 64 pages scanned version

    Complete list of publications

    You can retrieve my complete list of publications as pdf-file.

    A not so short CV


    Christian Berg
    Professor, dr. phil.
    Institute for Mathematical Sciences
    University of Copenhagen
    DK-2100 Copenhagen {\O}
    Phone:	(+45) 3532 0777

    Teaching spring term 1999

    Teaching spring term 2000

    Teaching in the fall term 2000

    Teaching in the spring term 2001

    Teaching in the fall term 2001

    No teaching in the spring term 2002

    Teaching in the fall term 2002

    Teaching in the spring term 2003

    Teaching in the fall term 2003

    Teaching in the spring term 2004

    Teaching in the fall term 2004

    Teaching in the spring term 2005

    Teaching in the fall term 2005

    The moment problem and orthogonal polynomials. This is a graduate course from November 14 to January 27, 2006 (Block 2A) Homepage

    Teaching in the spring term 2006

    Teaching in the academic year 2006-2007

    Teaching in the academic year 2007-2008

    Teaching in the academic year 2008-2009

    Teaching in the academic year 2009-2010

    Teaching in the academic year 2010-2011