New Examples of Convolutions and Non-Commutative Central Limit Theorems

Marek Bożejko; Janusz Wysoczański

Banach Center Publications (1998)

  • Volume: 43, Issue: 1, page 95-103
  • ISSN: 0137-6934

Abstract

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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.

How to cite

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Bożejko, Marek, and Wysoczański, Janusz. "New Examples of Convolutions and Non-Commutative Central Limit Theorems." Banach Center Publications 43.1 (1998): 95-103. <http://eudml.org/doc/208868>.

@article{Bożejko1998,
abstract = {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.},
author = {Bożejko, Marek, Wysoczański, Janusz},
journal = {Banach Center Publications},
keywords = {noncommutative central limit theorems; Cauchy transform; Nevanlinna theorem; -transform; multiplicative -weakly continuous transformation; dilations of measures; Voiculescu convolution; Boolean free convolution; -convoluton},
language = {eng},
number = {1},
pages = {95-103},
title = {New Examples of Convolutions and Non-Commutative Central Limit Theorems},
url = {http://eudml.org/doc/208868},
volume = {43},
year = {1998},
}

TY - JOUR
AU - Bożejko, Marek
AU - Wysoczański, Janusz
TI - New Examples of Convolutions and Non-Commutative Central Limit Theorems
JO - Banach Center Publications
PY - 1998
VL - 43
IS - 1
SP - 95
EP - 103
AB - 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.
LA - eng
KW - noncommutative central limit theorems; Cauchy transform; Nevanlinna theorem; -transform; multiplicative -weakly continuous transformation; dilations of measures; Voiculescu convolution; Boolean free convolution; -convoluton
UR - http://eudml.org/doc/208868
ER -

References

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  1. [AkG] N. I. Akhiezer and I. M. Glazman, Theory of Linear Operators in Hilbert Space, Ungar, New York, 1963. 
  2. [BLS] M. Bożejko, M. Leinert and R. Speicher, Convolution and limit theorems for conditionally free random variables, Pacific J. Math. 175, No. 2 (1996), 357-388. Zbl0874.60010
  3. [BSp1] M. Bożejko and R. Speicher, Interpolation between bosinic and fermionic relations given by generalized Brownian motions, Math. Z. 222 (1996), 135-160. 
  4. [BSp2] M. Bożejko, B. Kümmerer and R. Speicher, q-Gaussian Processes: Non-commutative and Classical Aspects, Comm. Math. Phys. 185 (1997), 129-154. 
  5. [Ma] H. Maassen, Addition of Freely Independent Random Variables, J. Funct. Anal. 106 No. 2 (1992), 409-438. Zbl0784.46047
  6. [Sp] R. Speicher, Multiplicative functions on the lattice of non-crossing partitions and free convolution, Math. Ann. 298 (1994), 611-628. Zbl0791.06010

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