Multiplicative Systems on Ultra-Metric Spaces

Memic, Nacima. "Multiplicative Systems on Ultra-Metric Spaces." Mathematica Balkanica New Series 24.3-4 (2010): 275-284. <http://eudml.org/doc/11348>.

@article{Memic2010,
abstract = {AMS Subj. Classification: MSC2010: 42C10, 43A50, 43A75We perform analysis of certain aspects of approximation in multiplicative systems that appear as duals of ultrametric structures, e.g. in cases of local fields, totally disconnected Abelian groups satisfying the second axiom of countability or more general ultrametric spaces that do not necessarily possess a group structure. Using the fact that the unit sphere of a local field is a Vilenkin group, we introduce a new concept of differentiation in the field of p-adic numbers. Some well known convergence tests are generalized to unbounded Vilenkin groups, i.e. to the setting where the standard boundedness assumption related to the sequence of subgroups generating the underlying topology is absent. A new Fourier multiplier theorem for Hardy spaces on such locally compact groups is obtained. The strong Lq, q > 1, and weak L1 boundedness of Fourier partial sums operators in the system constructed on more general ultrametric spaces is proved.},
author = {Memic, Nacima},
journal = {Mathematica Balkanica New Series},
keywords = {P-adic Derivative; Fourier Multiplier; Multiplicative System; Ultrametric Space; -adic derivative; Vilenkin group; Fourier multiplier; multiplicative system; ultra-metric space},
language = {eng},
number = {3-4},
pages = {275-284},
publisher = {Bulgarian Academy of Sciences - National Committee for Mathematics},
title = {Multiplicative Systems on Ultra-Metric Spaces},
url = {http://eudml.org/doc/11348},
volume = {24},
year = {2010},
}

TY - JOUR
AU - Memic, Nacima
TI - Multiplicative Systems on Ultra-Metric Spaces
JO - Mathematica Balkanica New Series
PY - 2010
PB - Bulgarian Academy of Sciences - National Committee for Mathematics
VL - 24
IS - 3-4
SP - 275
EP - 284
AB - AMS Subj. Classification: MSC2010: 42C10, 43A50, 43A75We perform analysis of certain aspects of approximation in multiplicative systems that appear as duals of ultrametric structures, e.g. in cases of local fields, totally disconnected Abelian groups satisfying the second axiom of countability or more general ultrametric spaces that do not necessarily possess a group structure. Using the fact that the unit sphere of a local field is a Vilenkin group, we introduce a new concept of differentiation in the field of p-adic numbers. Some well known convergence tests are generalized to unbounded Vilenkin groups, i.e. to the setting where the standard boundedness assumption related to the sequence of subgroups generating the underlying topology is absent. A new Fourier multiplier theorem for Hardy spaces on such locally compact groups is obtained. The strong Lq, q > 1, and weak L1 boundedness of Fourier partial sums operators in the system constructed on more general ultrametric spaces is proved.
LA - eng
KW - P-adic Derivative; Fourier Multiplier; Multiplicative System; Ultrametric Space; -adic derivative; Vilenkin group; Fourier multiplier; multiplicative system; ultra-metric space
UR - http://eudml.org/doc/11348
ER -