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1
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Completely positive maps on Coxeter groups and the ultracontractivity of the q-Ornstein-Uhlenbeck semigroup

100%
Bożejko M.
Banach Center Publications
|
1998
|
tom 43
|
nr 1
87-93
2
Content available remote

Remarks on q-CCR relations for |q| > 1

100%
Bożejko M.
Banach Center Publications
|
2007
|
tom 78
|
nr 1
59-67
EN
In this paper we give a construction of operators satisfying q-CCR relations for q > 1: $A(f)A*(g) - A*(g)A(f) = q^{N}⟨f,g⟩I$ and also q-CAR relations for q < -1: $B(f)B*(g) + B*(g)B(f) = |q|^{N}⟨f,g⟩I$, where N is the number operator on a suitable Fock space $ℱ_{q}(𝓗 )$ acting as Nx₁ ⊗ ⋯ ⊗ xₙ = nx₁ ⊗ ⋯ ⊗xₙ. Some applications to combinatorial problems are also given.
3
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A note on certain partial sum operators

64%
Bożejko M., Fendler G.
Banach Center Publications
|
2006
|
tom 73
|
nr 1
117-225
EN
We show that for the t-deformed semicircle measure, where 1/2 < t ≤ 1, the expansions of $L_p$ functions with respect to the associated orthonormal polynomials converge in norm when 3/2 < p < 3 and do not converge when 1 ≤ p < 3/2 or 3 < p. From this we conclude that natural expansions in the non-commutative $L_p$ spaces of free group factors and of free commutation relations do not converge for 1 ≤ p < 3/2 or 3 < p.
4
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Generalized q-deformed Gaussian random variables

64%
Bożejko M., Yoshida H.
Banach Center Publications
|
2006
|
tom 73
|
nr 1
127-140
EN
We produce generalized q-Gaussian random variables which have two parameters of deformation. One of them is, of course, q as for the usual q-deformation. We also investigate the corresponding Wick formulas, which will be described by some joint statistics on pair partitions.
5
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New Examples of Convolutions and Non-Commutative Central Limit Theorems

64%
Bożejko M., Wysoczański J.
Banach Center Publications
|
1998
|
tom 43
|
nr 1
95-103
EN
A family of transformations on the set of all probability measures on the real line is introduced, which makes it possible to define new examples of convolutions. The associated central limit theorems are studied, and examples of the limit measures, related to the classical, free and boolean convolutions, are shown.
6
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Topics on Meixner families

64%
Bożejko M., Demni N.
Banach Center Publications
|
2010
|
tom 89
|
nr 1
61-74
EN
We shed some light on the inter-connections between different characterizations leading to the classical Meixner family. This allows us to give free analogs of both Sheffer's and Al-Salam and Chihara's characterizations in the classical case by the use of the free derivative operator. The paper closes with a discussion of the q-deformed case, |q| < 1.
7
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Littlewood functions, Hankel multipliers and power bounded operators on a Hilbert space

50%
Bożejko M.
Colloquium Mathematicum
|
1987
|
tom 51
|
nr 1
35-42
8
Content available remote

Positive-definite kernels, length functions on groups and a noncommutative von Neumann inequality

50%
Bożejko M.
Studia Mathematica
|
1989-1990
|
tom 95
|
nr 2
107-118
9
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Sets of uniqueness on noncommutative locally compact groups. II

44%
Bożejko M.
Colloquium Mathematicum
|
1979
|
tom 42
|
nr 1
39-41
10
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Some aspects of harmonic analysis on free groups

38%
Bożejko M.
Colloquium Mathematicum
|
1979
|
tom 41
|
nr 2
265-271
11
Content available remote

A new group algebra and lacunary sets in discrete noncommutative groups

32%
Bożejko M.
Studia Mathematica
|
1981
|
tom 70
|
nr 2
165-175
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