A Family of Horn-Bernstein Functions

Autor: Christian Berg, Henrik L. Pedersen

Publikováno v: Experimental Mathematics. :1-9

A family of recently investigated Bernstein functions is revisited and those functions for which the derivatives are logarithmically completely monotonic are identified. This leads to the definition of a class of Bernstein functions, which we propose

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::27d0d2738321f18557038967dbc26791
https://doi.org/10.1080/10586458.2021.1980460

Filled Julia Sets of Chebyshev Polynomials

Autor: Carsten Lunde Petersen, Christian Henriksen, Jacob S. Christiansen, Henrik L. Pedersen

Publikováno v: Christiansen, J S, Henriksen, C, Pedersen, H L & Petersen, C L 2021, ' Filled Julia Sets of Chebyshev Polynomials ', Journal of Geometric Analysis . https://doi.org/10.1007/s12220-021-00716-y
Christiansen, J S, Henriksen, C, Pedersen, H L & Petersen, C L 2021, ' Filled Julia Sets of Chebyshev Polynomials ', Journal of Geometric Analysis, vol. 31, pp. 12250–12263 . https://doi.org/10.1007/s12220-021-00716-y

We study the possible Hausdorff limits of the Julia sets and filled Julia sets of subsequences of the sequence of dual Chebyshev polynomials of a non-polar compact set K in C and compare such limits to K. Moreover, we prove that the measures of maxim

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::30924ac2414313068759712fe8b178f6
https://orbit.dtu.dk/en/publications/6bdd8849-0965-494a-bd6f-fc527d8e4baf

Nielsen's beta function and some infinitely divisible distributions

Autor: Henrik L. Pedersen, Stamatis Koumandos, Christian Berg

Publikováno v: Berg, C, Koumandos, S & Pedersen, H L 2021, ' Nielsen's beta function and some infinitely divisible distributions ', Mathematische Nachrichten, vol. 294, no. 3, pp. 426-449 . https://doi.org/10.1002/mana.v294.3

We show that a large collection of special functions, in particular Nielsen's beta function, are generalized Stieltjes functions of order 2, and therefore logarithmically completely monotonic. This includes the Laplace transform of functions of the f

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c90b1a9b5993bfa53a825e3d69660778

Julia Sets of Orthogonal Polynomials

Autor: Henrik L. Pedersen, Christian Henriksen, Jacob S. Christiansen, Carsten Lunde Petersen

Publikováno v: Christiansen, J S, Henriksen, C, Pedersen, H L & Petersen, C L 2018, ' Julia Sets of Orthogonal Polynomials ', Potential Analysis, vol. 50, no. 3, pp. 401-413 . https://doi.org/10.1007/s11118-018-9687-5
Christiansen, J S, Henriksen, C, Pedersen, H L & Petersen, C L 2019, ' Julia Sets of Orthogonal Polynomials ', Potential Analysis, vol. 50, no. 3, pp. 401-413 . https://doi.org/10.1007/s11118-018-9687-5

For a probability measure with compact and non-polar support in the complex plane we relate dynamical properties of the associated sequence of orthogonal polynomials $\{P_n\}$ to properties of the support. More precisely we relate the Julia set of $P

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::059a8cb89bd4ff761c730d65423455b2
https://orbit.dtu.dk/en/publications/4005465a-25c4-4087-8622-9015c24706f4

Turán type inequalities for the partial sums of the generating functions of Bernoulli and Euler numbers

Autor: Stamatis Koumandos, Henrik L. Pedersen

Publikováno v: Mathematische Nachrichten. 285:2129-2156

Turan type inequalities for the partial sums of the generating functions of the Bernoulli and Euler numbers are established. They are shown to follow from a general result relating Turan inequalities of partial sums with Turan inequalities of the cor

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::a3d36a18fc551fa2697260fc6f51600a
https://doi.org/10.1002/mana.201100299