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.
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.
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
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
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
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 ArXivaccess 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
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 ArXivaccess 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
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).
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:http://www.arkivformatematik.org/
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 http://www.austms.org.au/Publ/Jamsa/
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. (http://jipam.vu.edu.au) 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.
Christian Berg
Professor, dr. phil.
Institute for Mathematical Sciences
University of Copenhagen
DK-2100 Copenhagen {\O}
Phone: (+45) 3532 0777
email: berg@math.ku.dk
