Christian Berg

Research output

Research output per year 1979 1993 1994 1995 2001 2002 2005 2006 2008 2011 2018

• 66 Journal article
• 6 Book chapter
• 2 Anthology
• 2 Literature review
• 3 More
  • 1 Book
  • 1 Compendium/lecture notes
  • 1 Article in proceedings

Research output per year

Research output per year

Search results

• 2018

  Inverse of Infinite Hankel Moment Matrices

  Berg, C. & Szwarc, R., 2018, In: Symmetry, Integrability and Geometry: Methods and Applications. 14, 48 p., 109.

  Research output: Contribution to journal › Journal article › Research › peer-review

  • Moment Problem 100%
  • Matrix (Mathematics) 100%
  • Moment Matrix 100%
  • Hankel 100%
  • Indeterminate 75%
  1 Citation (Scopus)

• Orthogonal expansions related to compact Gelfand pairs

  Berg, C., Peron, A. P. & Porcu, E., 2018, In: Expositiones Mathematicae. 36, 3-4, p. 259-277

  Research output: Contribution to journal › Journal article › Research › peer-review

  • Orthogonal Expansion 100%
  • Gelfand Pairs 100%
  • Uniformly Convergent 33%
  • Neutral Element 33%
  • Fourier Expansion 33%
  5 Citations (Scopus)

• Schoenberg's theorem for real and complex Hilbert spheres revisited

  Berg, C., Peron, A. P. & Porcu, E., Apr 2018, In: Journal of Approximation Theory. 228, p. 58-78

  Research output: Contribution to journal › Journal article › Research › peer-review

  • Unit Disk 100%
  • Coefficient Function 100%
  • Choquet Theory 100%
  • Rodrigues Formula 100%
  • Closed Unit 100%
  10 Citations (Scopus)
• 2017

  From Schoenberg Coefficients to Schoenberg Functions

  Berg, C. & Porcu, E., 1 Apr 2017, In: Constructive Approximation. 45, 2, p. 217-241

  Research output: Contribution to journal › Journal article › Research › peer-review

  • Positive Definite 100%
  • Product Space 100%
  • Schoenberg 100%
  • Stochastic Process 50%
  • Covariance Function 50%
  40 Citations (Scopus)

• On a Family of Functions Studied by Bhatia and Jain

  Berg, C., 3 Apr 2017, In: Experimental Mathematics. 26, 2, p. 241-246

  Research output: Contribution to journal › Journal article › Research › peer-review

  • Completely Monotonic Function 100%
  • Matrix-assisted Pulsed Laser Evaporation (MAPLE) 100%
  • Positive Parameter 100%
  • Parameter Values 100%

• Symmetric moment problems and a conjecture of Valent

  Berg, C. & Szwarc, R., 2017, In: Sbornik: Mathematics. 208, 3, p. 335-359

  Research output: Contribution to journal › Journal article › Research › peer-review

  • Romanov 100%
  • Moment Problem 100%
  • Hamburger Moment Problem 50%
  • Birth-death Process 50%
  • Stieltjes Moment Problem 50%
  2 Citations (Scopus)
• 2015

  A determinant characterization of moment sequences with finitely many mass points

  Berg, C. & Szwarc, R., 3 Aug 2015, In: Linear and Multilinear Algebra. 63, 8, p. 1568-1576

  Research output: Contribution to journal › Journal article › Research › peer-review

  • Point Mass 100%
  • Hankel Matrix 100%
  • Moment Sequence 100%
  • Discrete Measures 33%
  • Positive Semidefinite 33%
  10 Citations (Scopus)

• Asymptotic behaviour of the Urbanik semigroup

  Berg, C. & Luis Lopez, J., 1 Jul 2015, In: Journal of Approximation Theory. 195, p. 109-121

  Research output: Contribution to journal › Journal article › Research › peer-review

  • Semigroup 100%
  • Asymptotic Behavior 100%
  • Convolution 66%
  • Indeterminate 33%
  • Natural Number 33%
  5 Citations (Scopus)

• Open problems

  Berg, C., 15 Feb 2015, In: Integral Transforms and Special Functions. 26, 2, p. 90-95

  Research output: Contribution to journal › Journal article › Research › peer-review

  2 Citations (Scopus)
• 2014

  On the order of indeterminate moment problems

  Berg, C. & Szwarc, R., 15 Jan 2014, In: Advances in Mathematics. 250, p. 105-143

  Research output: Contribution to journal › Journal article › Research › peer-review

  • Indeterminate Moment Problem 100%
  • Orthonormal Polynomials 50%
  • Entire Function 50%
  • Recurrence Coefficients 50%
  • Exponent of Convergence 50%
  9 Citations (Scopus)
• 2013

  Complete Monotonicity of a Difference Between the Exponential and Trigamma Functions and Properties Related to a Modified Bessel Function

  Qi, F. & Berg, C., Nov 2013, In: Mediterranean Journal of Mathematics. 10, 4, p. 1685–1696

  Research output: Contribution to journal › Journal article › Research › peer-review

  • Trigamma Function 100%
  • Exponential Function 100%
  • Modified Bessel Function 100%
  • Complete Monotonicity 100%
  • I(1) 50%
  24 Citations (Scopus)

• On an Iteration Leading to a q-Analogue of the Digamma Function

  Berg, C. & Petersen, H. B., Aug 2013, In: Journal of Fourier Analysis and Applications. 19, 4, p. 762-776

  Research output: Contribution to journal › Journal article › Research › peer-review

  • Digamma Function 100%
  • Q-analogue 100%
  • Q-digamma Function 100%
  • Mellin Transform 50%
  • Continuous Density 50%
  1 Citation (Scopus)
• 2012

  A completely monotonic function used in an inequality of Alzer

  Berg, C. & Pedersen, H. L., 2012, In: Computational Methods and Function Theory. 12, p. 329-341

  Research output: Contribution to journal › Journal article › Research › peer-review

  • Completely Monotonic Function 100%
  • Stieltjes 100%
  • Integral Representation 100%
  • Stieltjes Transform 50%
  • Holomorphic Extension 50%
  5 Citations (Scopus)

• Derivation of an integral of Boros and Moll via convolution of Student t-densities

  Berg, C. & Vignat, C., Feb 2012, In: Ramanujan Journal. 27, 2, p. 147-150

  Research output: Contribution to journal › Journal article › Research › peer-review

  • Convolution 100%
  • Integral 100%
  2 Citations (Scopus)
• 2011

  A one-parameter family of pick functions defined by the gamma function and related to the volume of the unit ball in n-space

  Berg, C. & Pedersen, H. L., Jun 2011, In: Proceedings of the American Mathematical Society. 139, 6, p. 2121-2132 12 p.

  Research output: Contribution to journal › Journal article › Research › peer-review

  • One-parameter Family 100%
  • Pick Function 100%
  • Unit Ball 100%
  • Parameter Family 100%
  • Gamma Function 100%
  14 Citations (Scopus)

• A question by T. S. Chihara about shell polynomials and indeterminate moment problems

  Berg, C. & Christiansen, J. S., Oct 2011, In: Journal of Approximation Theory. 163, 10, p. 1449-1464

  Research output: Contribution to journal › Journal article › Research › peer-review

  • Indeterminate 100%
  • Moment Problem 100%
  • Polynomial 100%
  • Indeterminate Moment Problem 100%
  • Parameter Sequence 100%
  1 Citation (Scopus)

• Book review of Barry Simon: Szego's Theorem and its Descendants: Spectral Theory for L^2 Perturbations of Orthogonal Polynomials. Princeton University Press, 2010

  Berg, C., 2011, In: Journal of Approximation Theory. 163, 8, p. 1029-1034

  Research output: Contribution to journal › Literature review › Communication

• Fibonacci numbers, Euler’s 2-periodic continued fractions and moment sequences

  Berg, C. & Durán, A. J., Feb 2011, In: Fibonacci Quarterly. 49, p. 66-75

  Research output: Contribution to journal › Journal article › Research › peer-review

  • Periodic Continued Fractions 100%
  • 2-periodic 100%
  • Signed Measure 33%

• Fibonacci numbers and orthogonal polynomials

  Berg, C., Jul 2011, In: Arab Journal of Mathematical Sciences. 17, 2, p. 75-88

  Research output: Contribution to journal › Journal article › Research › peer-review

  • Orthogonal Polynomial 100%
  • Fibonacci numbers 100%
  • Integer Coefficient 50%
  • Jacobi Polynomials 50%
  • Hankel Matrix 50%
  6 Citations (Scopus)

• The smallest eigenvalue of Hankel matrices

  Berg, C. & Szwarc, R., Aug 2011, In: Constructive Approximation. 34, 1, p. 107-133

  Research output: Contribution to journal › Journal article › Research › peer-review

  • Hankel Matrix 100%
  • Smallest Eigenvalue 100%
  • Small Eigenvalue 100%
  • Stieltjes-Wigert Polynomials 33%
  • Any Order 33%
  19 Citations (Scopus)
• 2010

  On a fixed point in the metric space of normalized Hausdorff moment sequences

  Berg, C. & Beygmohammadi, M., 2010, In: Supplemento ai Rendiconti del Circolo matematico di Palermo. 82, p. 251-257

  Research output: Contribution to journal › Journal article › Research › peer-review

• On the density of the sum of two independent Student t-random vectors

  Berg, C. & Vignat, C., Jul 2010, In: Statistics & Probability Letters. 80, p. 1043-1055

  Research output: Contribution to journal › Journal article › Research › peer-review

  • Random Vector 100%
  • Independent Students 100%
  • Non-negative Integer 50%
  • Infinitely Divisible 50%
  • Infinite Series 50%
  7 Citations (Scopus)

• Positive polynomials and sums of squares by Murray Marshall. Mathematical Surveys and Monographs, Volume 146, AMS, Providence, RI 2008. ISBN 978-0-8218-4402-1: Book reviews

  Berg, C., 2010, In: Journal of Approximation Theory. 162, p. 236-238

  Research output: Contribution to journal › Literature review › Communication

  • Sum of Squares 100%
  • Monograph 100%
  • Positive Polynomials 100%
• 2009

  Bounds on Turán determinants

  Berg, C. & Szwarc, R., 2009, In: Journal of Approximation Theory. 161, p. 127-141

  Research output: Contribution to journal › Journal article › Research › peer-review

  8 Citations (Scopus)

• Børge Jessen, 19.6.1907-20.3.1993: Biography of Jessen

  Berg, C., 2009, In: Electronic Journal for History of Probability and Statistics. 5, 1, 15 p.

  Research output: Contribution to journal › Journal article › Communication

• Quantum Hilbert matrices and orthogonal polynomials

  Berg, C. & Andersen, J. E., 2009, In: Journal of Computational and Applied Mathematics. 233, p. 723-729

  Research output: Contribution to journal › Journal article › Research › peer-review

  7 Citations (Scopus)
• 2008

  Convexity of the median in the gamma distribution

  Berg, C. & Pedersen, H. L., 2008, In: Arkiv for Matematik. 46, 1, p. 1-6 6 p.

  Research output: Contribution to journal › Journal article › Research › peer-review

  5 Citations (Scopus)

• Iteration of the rational function z-1/z and a Hausdorff moment sequence

  Berg, C. & Durán, A. J., 2008, In: Expositiones Mathematicae. 26, p. 375-385

  Research output: Contribution to journal › Journal article › Research › peer-review

  1 Citation (Scopus)

• Linearization coefficients of Bessel polynomials and properties of Student-t distributions

  Berg, C. & Vignat, C., 2008, In: Constructive Approximation. 27, p. 15-32

  Research output: Contribution to journal › Journal article › Research › peer-review

  13 Citations (Scopus)

• On some results of Cufaro Petroni about Student t-processes

  Berg, C. & Vignat, C., 2008, In: Journal of Physics A: Mathematical and Theoretical (Print Edition). 41, 10 p.

  Research output: Contribution to journal › Journal article › Research › peer-review

  5 Citations (Scopus)

• Stieltjes-Pick-Bernstein-Schoenberg and their connection to complete monotonicity

  Berg, C., 2008, Positive Definite Functions: From Schoenberg to Space-Time Challenges. Mateu, J. & Porcu, E. (eds.). Dept. of Mathematics, University Jaume I, Castellon, Spain, p. 15-45

  Research output: Chapter in Book/Report/Conference proceeding › Book chapter › Research

• The Dagum family of isotropic correlation functions

  Berg, C., Mateu, J. & Porcu, E., 2008, In: Bernoulli. 14, 4, p. 1134-1149

  Research output: Contribution to journal › Journal article › Research › peer-review

  33 Citations (Scopus)

• The fixed point for a transformation of Hausdorff moment sequences and iteration of a rational function

  Berg, C. & Durán, A. J., 2008, In: Mathematica Scandinavica. 103, p. 11-39

  Research output: Contribution to journal › Journal article › Research › peer-review

  4 Citations (Scopus)
• 2007

  Complex Analysis

  Berg, C., 2007, 1. ed. Universitetsparken 5, 2100 København Ø: Universitetsbogladen. 190 p.

  Research output: Book/Report › Compendium/lecture notes

• Logarithmic order and type of indeterminate moment problems

  Berg, C., Pedersen, H. L. & Hayman, W., 2007, Proceedings of the international Conference "Difference Equations, Special Functions and Orthogonal Polynomials". Elaydi et al., S. (ed.). World Scientific, p. 51-79

  Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

• On powers of Stieltjes moment sequences, II

  Berg, C., 2007, In: Journal of Computational and Applied Mathematics. 199, p. 23-38

  Research output: Contribution to journal › Journal article › Research › peer-review

  15 Citations (Scopus)
• 2006

  Orthogonal Polynomials and analytic functions associated to positive definite matrices

  Berg, C. & Duran, A. J., 2006, In: Journal of Mathematical Analysis and Applications. 315, 5, p. 54-67

  Research output: Contribution to journal › Journal article › Research › peer-review

  5 Citations (Scopus)

• Ortogonale polynomier og Hilbertmatricen

  Berg, C., 2006, In: Normat - Nordisk Matematisk Tidsskrift. 54, 3, p. 116-133

  Research output: Contribution to journal › Journal article › Research › peer-review

• Some classes of completely montonic functions, II

  Alzer, H. & Berg, C., 2006, In: Ramanujan Journal. 11, p. 225-248

  Research output: Contribution to journal › Journal article › Research › peer-review

  49 Citations (Scopus)

• The Chen-Rubin conjecture in a continuous setting

  Berg, C. & Pedersen, H. L., 2006, In: Methods and Applications of Analysis. 13, 1, p. 63-88 26 p.

  Research output: Contribution to journal › Journal article › Research › peer-review
• 2005

  On a conjecture of Clark and Ismail

  Berg, C., Alzer, H. & Koumandos, S., 2005, In: Journal of Approximation Theory. 134, p. 102-113

  Research output: Contribution to journal › Journal article › Research › peer-review

  8 Citations (Scopus)

• On powers on Stieltjes moment sequences, I

  Berg, C., 2005, In: Journal of Theoretical Probability. 18, p. 871-889

  Research output: Contribution to journal › Journal article › Research › peer-review

  24 Citations (Scopus)

• Proceedings of the Seventh International Symposium on Orthogonal Polynomials, Special Functions and Applications

  Berg, C. (Editor), Christiansen, J. S. (Editor) & Pedersen, H. L. (Editor), 2005, 538 p. (Journal of Computational and Applied Mathematics, Vol. 178).

  Research output: Book/Report › Anthology › Research › peer-review

• Some transformations of Hausdorff moment sequences and harmonic numbers

  Berg, C. & Duran, A. J., 2005, In: Canad. J. Math.. 57, p. 941-960

  Research output: Contribution to journal › Journal article › Research › peer-review

  7 Citations (Scopus)

• Theory and Applications of Special Functions: On a generalized Gamma convolution related to the q-calculus

  Berg, C., 2005, Berlin. 15 p. (Developments of Mathematics, Vol. 13).

  Research output: Book/Report › Anthology › Research › peer-review
• 2004

  A transformation from Hausdorff to Stieltjes moment sequences

  Berg, C. & Duran, A. J., 2004, In: Arkiv for Matematik. 42, p. 239-257

  Research output: Contribution to journal › Journal article › Research › peer-review

  26 Citations (Scopus)

• Correction to a paper by A.G. Pakes

  Berg, C., 2004, In: Journal of the Australian Mathematical Society. 76, p. 67-73

  Research output: Contribution to journal › Journal article › Research › peer-review

  2 Citations (Scopus)

• Integral representation of some functions related to the gamma function

  Berg, C., 2004, In: Mediterranean Journal of Mathematics. 1, p. 433-439

  Research output: Contribution to journal › Journal article › Research › peer-review
• 2002

  Kompleks Funktionsteori

  Berg, C., 2002, Kompleks Funktionsteori. København: Universitetsbogladen, p. 156

  Research output: Chapter in Book/Report/Conference proceeding › Book chapter › Education

• Pick functions related to the Gamma function

  Berg, C. & Pedersen, H. L., 2002, In: Rocky Mountain Journal of Mathematics. 32, 2, p. 507-525

  Research output: Contribution to journal › Journal article › Research › peer-review

  23 Citations (Scopus)