# Multiplicative Systems on Ultra-Metric Spaces

Mathematica Balkanica New Series (2010)

- Volume: 24, Issue: 3-4, page 275-284
- ISSN: 0205-3217

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topMemic, 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 -

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