Publications
Monographs
Positive Definite and Definitizable Functions.
Berlin: Akademie Verlag, 1994.
Errata (Version September 19, 2019)
(with Torben Maack Bisgaard)
Characteristic Functions and Moment Sequences. Vol. I..
Nova Science, 2000.
Multivariate Characteristic and Correlation Functions.
De Gruyter, p. 366, 2013.
Errata (Version May 19, 2022)
Papers
(with J. Bartholomäus, S. Wunderlich)
Identification of Suspicious Semiconductor Devices Using Independent Component Analysis with Dimensionality Reduction.
30th Annual IEEE/SEMI® Advanced Semiconductor Manufacturing Conference-ASMC, 2019.
(with G. Berschneider) Spectral Theory of Stationary Random Fields and their Generalizations.
A Short Historical Survey.
In: D. Alpay, B. Kirstein, (eds.), Indefinite Inner Product Spaces, Schur Analysis, and Differential Equations. A Volume Dedicated to Heinz Langer. Birkhäuser/Springer, Basel, 2018, 217-236
(with S. Vock, C. Hengst, R. Schäfer, L. Schultz and V. Neu) The role of the inhomogeneous demagnetizing field on the reversal mechanism in nanowire arrays.
Journal of Physics D: Applied Physics, Volume 50, Number 47 (2017)
(with S. Vock et al.)
Magnetic vortex observation in FeCo nanowires by quantitative Magnetic Force Microscopy.
Applied Physics Letters, 105/17 (2014).
(with G. Berschneider)
On a theorem of Karhunen and related moment problems and quadrature formulae.
Proceedings IWOTA 2010
published in: Operator Theory: Advances and Applications, Vol. 221, 171-185 (2012).
(with S. Vock et al.)
Quantitative Magnetic Force Microscopy study of the diameter evolution of bubble domains in a (Co/Pd)80 multilayer.
IEEE Transactions on Magnetics, Vol. 47, No. 10 (2011).
(with M. Kücken)
Lotteries and Truncated Binomial Coefficients
Math. Nachr. 284(11-12), 1538-1546 (2011).
The data mentioned in the paper can be downloaded here: Lottery
Correlation functions of intrinsically stationary random fields
Operator Theory: Advances and Applications, The Mark Krein Centennary Conference, Vol. 190, 451-470 (2009).
On the Extension Problem for Covariance Functions.
Published in: Positive Definite Functions: from Schoenberg to Space-Time Challenges, Universitat Jaume I. Dept. of Math. (2008).
On generalized correlation functions of intrinsically stationary processes of order k
Stat. & Prob. Letters, 78(18), 3381-3387 (2008), Link.
(with P. Gregori, E. Porcu and J. Mateu)
On potentially negative space time covariances obtained as sum of products of marginal ones.
Ann. Inst. Stat. Math. (2007).
(with Torben Maack Bisgaard)
On a lower bound for ∑j,k ∈ Zcj ck e -q(j-k)2
Tatra Mt. Math. Publ. 34, 339-342 (2006).
(with Torben Maack Bisgaard)
When does E(Xk·Xj) = E(Xk) ·E(Xj) imply independence?
Statist. Probab. Letters. 76, 1111-1116 (2006).
The Extension Problem for Positive Definite Functions. A Short Historical Survey.
Operator Theory: Advances and Applications, Vol. 163, 365-379 (2005).
(with H. Langer and M. Langer)
Continuations of Hermitian indefinite functions and corresponding canonical systems: an example.
Methods Funct. Anal. Topology, 10(1), 39–53 (2004).
(with S. Mitra and T. Gneiting)
Polynomial covariance functions on intervals.
Bernoulli 9(2), 229–241 (2003).
(with J.P.R. Christensen)
The dimension of the linear space spanned by all partial derivatives of a symmetric polynomial.
Math. Nachr. 241, 28–31 (2002).
(with T. Gneiting and M. Schlather)
Analogies and correspondences between variograms and covariance functions.
Advances in Appl. Prob. 33, 617–630 (2001).
(with T. M. Bisgaard and Zs. Páles)
A problem on determinants (Problem 10896).
Amer. Math. Monthly 108(8), p.770 (2001).
The relative error in the local limit theorem of de Moivre and Laplace (Problem 10876).
Amer. Math. Monthly 108(5), p.469 (2001).
Inequalities for binomial coefficients.
J. Math. An. and Appl. 236, 223–226 (1999).
Determinants, sums involving binomial coefficients, and moment sequences.
Analysis Mathematica 25, 133–146 (1999).
An elementary proof of Binet's formula for the gamma function.
Amer. Math. Monthly, 106(2), 157–158 (1999).
An inequality for the standard normal distribution (Problem 10709).
Amer. Math. Monthly, 106(1), p. 68 (1999).
(with T. Gneiting)
The characterization problem for isotropic covariance functions.
Math. Geology, 31(1), 105–111 (1999).
On the number of negative squares of certain functions.
Proceedings of the Colloquium held on the occasion of Professor Heinz Langer's 60th birthday. Operator Theory: Adv. and Appl., vol. 106, 337–353, Birkhäuser: Basel, 1998.
On unions of σ–fields. (Problem 10667).
Amer. Math. Monthly, 105(5), p. 465 (1998).
The number e once more (Problem 10650).
Amer. Math. Monthly 105(3), p. 271 (1998).
The remainder in the logarithm series. Solution of Problem 10539.
Amer. Math. Monthly 105(1), 77–78 (1998).
On a classical theorem in the theory of Fourier integrals.
Proc. Amer. Math. Soc. 126(3), 711–713 (1998).
Remarks on entire characteristic functions.
Math. Moravica, Spec. vol. Proc. IWAA, 297–300 (1997).
An inequality for the normal distribution (Problem 10611).
Amer. Math. Monthly, 104(7), p. 665 (1997).
(with H. Langer)
Is there a simple proof? (Problem 97–9).
SIAM Rev. 39(2), p. 318 (1997).
(with T. M. Bisgaard)
On the positive definiteness of certain functions.
Math. Nachr. 186,81–99 (1997)
On norm dependent positive definite functions.
Monatshefte für Math. 120, 319–325 (1995).
(with I. I. Kotlarski)
On a characterization problem of statistics.
Statistics 23, 85–93 (1992)
On separately polynomial functions.
Arch. Math. Vol. 59, 91–94 (1992).
A set of points related to nonnegative cosine polynomials (solution of Problems 6608(b)* and (c)* proposed by O. D. Anderson).
Amer. Math. Monthly 98(10), 966–967 (1991).
On measurable local homomorphisms.
Proc. Amer. Math. Soc. 112(2), 603–604 (1991).
Conditionally positive definite functions and unitary representations in π1 – spaces.
Math. Nachr. 146, 69–75 (1990).
(with H. Langer)
Definitizing polynomials of unitary and Hermitian operators in Pontrjagin spaces.
Math. Ann. 288, 231–243 (1990).
On a refinement of the Gelfand–Raikov theorem.
Math. Nachr. 150, 185–187 (1990).
New proof of Naimark's theorem on the existence of nonpositive invariant subspaces for commuting families of unitary operators in Pontryagin spaces.
Monatshefte für Math., 109, 153–156 (1990).
On common fixed points of linear contractions.
Proc. Amer. Math. Soc. 108(2), 565–566 (1990).
Characterization of locally bounded functions with a finite number of negative squares.
Acta Sci. Math. (Szeged) 53, 319–327 (1989).
Definisierbare Funktionen auf Gruppen.
Dissertationes Math., CCLXXXI, 83 pp. (1989).
Additivity of certain functionals and the construction of invariant integrals.
Math. Ann. 283, 573–581 (1989).
On continuity and decomposition of positive definite functions.
Math. Nachr. 140, 103–108 (1989).
(with C. Berg)
Functions with a finite number of negative squares on semigroups.
Monatshefte für Math. 107, 9–34 (1989).
Definitizability of certain functions and the existence of eigenvectors of unitary operators in Pontrjagin spaces.
Math. Nachr. 135, 67–72 (1988).
On the extension of positive definite functions.
Radovi Mat., Vol. 3, 235–240 (1987).
Decomposition of positive definite functions defined on a neighbourhood of the identity.
Monatshefte für Math. 104, 139–148 (1987).
(with W. Wolf)
Characterizing the distributions of the random vectors X1, X2, X3 by the distribution of the statistic (X1 – X3, X2 – X3).
Stability problems for stochastic models, Proc. 9th Int. Semin. Varna/Bulg. 1985, Lecture Notes Math. 1233, 172–177 (1987). W. Wolf)
Addendum to the paper "On the measurability of positive definite and conditionally positive definite functions".
Math. Nachr. 131, 345–347 (1987).
On measurable functions with a finite number of negative squares.
Acta Sci. Math. (Szeged) 50, 359–363 (1986).
(with W. Wolf)
Some remarks on the existence of density for weighted sums.
Published in: Probability distributions and mathematical statistics. (in russian) FAN USSR, 83–94 (1986).
Characterizing the distributions of the random variables X1, X2, X3 by the distribution of (X1 – X3, X2 – X3).
Probab. Th. Rel. Fields, 73, 43–49 (1986).
On the measurability of positive definite and conditionally positive definite functions.
Math. Nachr. 125, 239–242 (1986).
The extension problem for measurable positive definite functions.
Math. Zeitschrift 191, 475–478 (1986).
Einige Beiträge zur Theorie der positiv definiten Funktionen mit Anwendungen für Charakterisationsprobleme der mathematischen Statistik.
Wiss. Sitzungen zur Stochastik, WSS–01/85 (1985).
Indefinite functions on commutative groups.
Monatshefte für Math. 100, 223–238 (1985).
(with W. Wolf)
Über die Wiederherstellung der Ausgangsverteilung durch die Statistik (X1 – X3, X2 – X3).
Math. Operationsforsch. Statist. Ser. Statist. 16(2), 233–241 (1985).
Über die Nullstellenmenge von charakteristischen Funktionen.
Math. Nachr. 121, 33–40 (1985).
On bounded functions with a finite number of negative squares.
Monatshefte für Math. 99, 223–234 (1985).
Einige Bemerkungen über die Fortsetzung positiv definiter Funktionen.
Zeitschrift für An. und Anw. 3(5), 435–440 (1984).
Megjegyzések végesdimenziós algebrákon értelmezett szemi–differenciál operátorokról.
Acta Iuv. Univ. Debreceniensis, VIII:2, 179–185 (1979).