# 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

## Access Full Article

top## Abstract

top## How to cite

topBożejko, 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

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

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.