Differential independence via an associative product of infinitely many linear functionals

Takahiro Hasebe. "Differential independence via an associative product of infinitely many linear functionals." Colloquium Mathematicae 124.1 (2011): 79-94. <http://eudml.org/doc/284234>.

@article{TakahiroHasebe2011,
abstract = {We generalize the infinitesimal independence appearing in free probability of type B in two directions: to higher order derivatives and other natural independences: tensor, monotone and Boolean. Such generalized infinitesimal independences can be defined by using associative products of infinitely many linear functionals, and therefore the associated cumulants can be defined. These products can be seen as the usual natural products of linear maps with values in formal power series.},
author = {Takahiro Hasebe},
journal = {Colloquium Mathematicae},
keywords = {free probability of type B; tensor independence; monotone independence; Boolean independence},
language = {eng},
number = {1},
pages = {79-94},
title = {Differential independence via an associative product of infinitely many linear functionals},
url = {http://eudml.org/doc/284234},
volume = {124},
year = {2011},
}

TY - JOUR
AU - Takahiro Hasebe
TI - Differential independence via an associative product of infinitely many linear functionals
JO - Colloquium Mathematicae
PY - 2011
VL - 124
IS - 1
SP - 79
EP - 94
AB - We generalize the infinitesimal independence appearing in free probability of type B in two directions: to higher order derivatives and other natural independences: tensor, monotone and Boolean. Such generalized infinitesimal independences can be defined by using associative products of infinitely many linear functionals, and therefore the associated cumulants can be defined. These products can be seen as the usual natural products of linear maps with values in formal power series.
LA - eng
KW - free probability of type B; tensor independence; monotone independence; Boolean independence
UR - http://eudml.org/doc/284234
ER -