A general differentiation theorem for multiparameter additive processes

Ryotaro Sato. "A general differentiation theorem for multiparameter additive processes." Colloquium Mathematicae 91.1 (2002): 143-155. <http://eudml.org/doc/284354>.

@article{RyotaroSato2002,
abstract = {Let $(L,||·||_\{L\})$ be a Banach lattice of equivalence classes of real-valued measurable functions on a σ-finite measure space and $T = \{T(u): u = (u₁,...,u_\{d\}), u_\{i\} > 0, 1 ≤ i ≤ d\}$ be a strongly continuous locally bounded d-dimensional semigroup of positive linear operators on L. Under suitable conditions on the Banach lattice L we prove a general differentiation theorem for locally bounded d-dimensional processes in L which are additive with respect to the semigroup T.},
author = {Ryotaro Sato},
journal = {Colloquium Mathematicae},
keywords = {ergodic theorem; differentiation; multiparameter additive processes; Banach lattice of measurable functions; differentiation theorem; semigroup of positive linear contractions},
language = {eng},
number = {1},
pages = {143-155},
title = {A general differentiation theorem for multiparameter additive processes},
url = {http://eudml.org/doc/284354},
volume = {91},
year = {2002},
}

TY - JOUR
AU - Ryotaro Sato
TI - A general differentiation theorem for multiparameter additive processes
JO - Colloquium Mathematicae
PY - 2002
VL - 91
IS - 1
SP - 143
EP - 155
AB - Let $(L,||·||_{L})$ be a Banach lattice of equivalence classes of real-valued measurable functions on a σ-finite measure space and $T = {T(u): u = (u₁,...,u_{d}), u_{i} > 0, 1 ≤ i ≤ d}$ be a strongly continuous locally bounded d-dimensional semigroup of positive linear operators on L. Under suitable conditions on the Banach lattice L we prove a general differentiation theorem for locally bounded d-dimensional processes in L which are additive with respect to the semigroup T.
LA - eng
KW - ergodic theorem; differentiation; multiparameter additive processes; Banach lattice of measurable functions; differentiation theorem; semigroup of positive linear contractions
UR - http://eudml.org/doc/284354
ER -