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1
Content available remote

Probability measures corresponding to Aval numbers

100%
Młotkowski W.
Colloquium Mathematicum
|
2012
|
tom 129
|
nr 2
189-202
EN
We describe the class of probability measures whose moments are given in terms of the Aval numbers. They are expressed as the multiplicative free convolution of measures corresponding to the ballot numbers $(m-k)/(m+k) \binom{m+k}{m}$.
2
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Some class of polynomial hypergroups

100%
Młotkowski W.
Banach Center Publications
|
2006
|
tom 73
|
nr 1
357-362
EN
We provide explicit formulas for linearizing coefficients for some class of orthogonal polynomials.
3
Content available remote

Type-dependent positive definite functions on free products of groups

100%
Młotkowski W.
Colloquium Mathematicum
|
1993
|
tom 64
|
nr 1
41-54
4
Content available remote

Operator-valued version of conditionally free product

100%
Młotkowski W.
Studia Mathematica
|
2002
|
tom 153
|
nr 1
13-30
EN
We present an operator-valued version of the conditionally free product of states and measures, which in the scalar case was studied by Bożejko, Leinert and Speicher. The related combinatorics and limit theorems are provided.
5
Content available remote

Irreducible representations of free products of infinite groups

100%
Młotkowski W.
Colloquium Mathematicum
|
1996
|
tom 69
|
nr 2
193-211
6
Content available remote

Nonnegative linearization for orthogonal polynomials with eventually constant Jacobi parameters

100%
Młotkowski W.
Banach Center Publications
|
2010
|
tom 89
|
nr 1
223-230
EN
We study the nonnegative product linearization property for polynomials with eventually constant Jacobi parameters. For some special cases a necessary and sufficient condition for this property is provided.
7
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Free powers of the free Poisson measure

64%
Hinz M., Młotkowski W.
Colloquium Mathematicum
|
2011
|
tom 123
|
nr 2
285-290
EN
We compute moments of the measures $(ϖ^{⊠ p})^{⊞ t}$, where ϖ denotes the free Poisson law, and ⊞ and ⊠ are the additive and multiplicative free convolutions. These moments are expressed in terms of the Fuss-Narayana numbers.
8
Content available remote

Free cumulants of some probability measures

64%
Hinz M., Młotkowski W.
Banach Center Publications
|
2007
|
tom 78
|
nr 1
165-170
9
Content available remote

Limit Measures Related to the Conditionally Free Convolution

64%
Hinz M., Młotkowski W.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2008
|
tom 56
|
nr 1
75-81
EN
We describe the limit measures for some class of deformations of the free convolution, introduced by A. D. Krystek and Ł. J. Wojakowski. In particular, we provide a counterexample to a conjecture from their paper.
10
Content available remote

Symmetrization of probability measures, pushforward of order 2 and the Boolean convolution

64%
Młotkowski W., Sakuma N.
Banach Center Publications
|
2011
|
tom 96
|
nr 1
271-276
EN
We study relations between the Boolean convolution and the symmetrization and the pushforward of order 2. In particular we prove that if μ₁,μ₂ are probability measures on [0,∞) then $(μ₁ ⨄ μ₂)^{s} = μ₁^{s} ⨄ μ₂^{s}$ and if ν₁,ν₂ are symmetric then $(ν₁ ⨄ ν₂)^{(2)} = ν₁^{(2)} ⨄ ν₂^{(2)}$. Finally we investigate necessary and sufficient conditions under which the latter equality holds.
11
Content available remote

Multiplicative free square of the free Poisson measure and examples of free symmetrization

64%
Hinz M., Młotkowski W.
Colloquium Mathematicum
|
2010
|
tom 119
|
nr 1
127-136
EN
We compute the moments and free cumulants of the measure $ρ_t: = π_t ⊠ π_t$, where $π_t$ denotes the free Poisson law with parameter t > 0. We also compute free cumulants of the symmetrization of $ρ_t$. Finally, we introduce the free symmetrization of a probability measure on ℝ and provide some examples.
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