<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>1409-2433</journal-id>
<journal-title><![CDATA[Revista de Matemática Teoría y Aplicaciones]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. Mat]]></abbrev-journal-title>
<issn>1409-2433</issn>
<publisher>
<publisher-name><![CDATA[Centro de Investigaciones en Matemática Pura y Aplicada (CIMPA) y Escuela de Matemática, San José, Costa Rica.]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1409-24332022000100039</article-id>
<article-id pub-id-type="doi">10.15517/rmta.v29i1.45440</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Aproximación trigonométrica en espacios Lipschitz]]></article-title>
<article-title xml:lang="en"><![CDATA[Trigonometric approximation in Lipschitz spaces]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Martínez-Guzmán]]></surname>
<given-names><![CDATA[Gerardo]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Loranca]]></surname>
<given-names><![CDATA[María Beatríz Bernábe]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Gómez]]></surname>
<given-names><![CDATA[Mariano Larios]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Vanoye]]></surname>
<given-names><![CDATA[Jorge Ruiz]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Benemérita Universidad Autónoma de Puebla Facultad de Ciencias de la Computación ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Benemérita Universidad Autónoma de Puebla Facultad de Ciencias de la Computación ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Benemérita Universidad Autónoma de Puebla Facultad de Ciencias de la Computación ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af4">
<institution><![CDATA[,Universidad Politécnica de Pachuca  Departamento de Ingeniería de Software]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2022</year>
</pub-date>
<volume>29</volume>
<numero>1</numero>
<fpage>39</fpage>
<lpage>52</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S1409-24332022000100039&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S1409-24332022000100039&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S1409-24332022000100039&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen La aproximación por polinomios trigonométricos generalizados para funciones de Lipschitz, definidas en ciertos grupos depende de algunas propiedades de la métrica definida en el grupo. Métricas donde esta aproximación es posible son llamadas Lipschitz compatibles. En este trabajo damos para cierta clase de grupos, condiciones donde las métricas Lipschitz compatibles son acotadamente equivalentes, es decir, generan el mismo espacio de Lipschitz. En particular, para el grupo multiplicativo de números complejos con norma uno las condiciones son necesarias y suficientes para que las métricas Lipschitz compatibles sean acotadamente equivalentes.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract The approximation by generalized trigonometric polynomials for Lipschitz defined functions in certain groups depends on some properties of the group defined metric. Metrics which allow this approximation are called Lipschitz compatible. In this work we give for certain class of groups, conditions under which Lipschitz compatible metrics are boundedly equivalent, i.e., they generate the same Lipschitz space. In particular, for the multiplicative group of modulus one complex numbers the conditions are necessary and sufficient for the compatible Lipschitz metrics to be boundedly equivalent.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Lipschitz spaces]]></kwd>
<kwd lng="en"><![CDATA[invariant metrics]]></kwd>
<kwd lng="en"><![CDATA[trigonometric polynomials]]></kwd>
<kwd lng="en"><![CDATA[topological groups]]></kwd>
<kwd lng="en"><![CDATA[dual space.]]></kwd>
<kwd lng="es"><![CDATA[espacios de Lipschitz]]></kwd>
<kwd lng="es"><![CDATA[métricas invariantes]]></kwd>
<kwd lng="es"><![CDATA[polinomios trigonométricos]]></kwd>
<kwd lng="es"><![CDATA[grupos topológicos]]></kwd>
<kwd lng="es"><![CDATA[espacio dual.]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[H]]></surname>
<given-names><![CDATA[Abels.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Reductive groups as metric spaces]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Müller]]></surname>
<given-names><![CDATA[T,W,]]></given-names>
</name>
</person-group>
<source><![CDATA[Groups: topological, Combinatorial and arithmetic aspects]]></source>
<year>2004</year>
<page-range>1-20</page-range><publisher-loc><![CDATA[Cambridge ]]></publisher-loc>
<publisher-name><![CDATA[Cambridge University Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[E]]></surname>
<given-names><![CDATA[Hewitt]]></given-names>
</name>
<name>
<surname><![CDATA[K,A]]></surname>
<given-names><![CDATA[Ross.]]></given-names>
</name>
</person-group>
<collab>Grundlehren der Mathematischen Wissenschaften 115</collab>
<source><![CDATA[Abstract Harmonic Analysis, Vol. I, Structure of Topological Groups, Integration Theory, Group Representations]]></source>
<year>1979</year>
<edition>2nd Edition</edition>
<publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[L]]></surname>
<given-names><![CDATA[Leindler]]></given-names>
</name>
<name>
<surname><![CDATA[A]]></surname>
<given-names><![CDATA[Meir]]></given-names>
</name>
<name>
<surname><![CDATA[V]]></surname>
<given-names><![CDATA[Totik.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On approximation of continuous functions in Lipschitz norms]]></article-title>
<source><![CDATA[Acta. Math. Hung.]]></source>
<year>1985</year>
<volume>45</volume>
<numero>3-4</numero>
<issue>3-4</issue>
<page-range>441-3</page-range></nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[H]]></surname>
<given-names><![CDATA[Reiter]]></given-names>
</name>
<name>
<surname><![CDATA[J,D]]></surname>
<given-names><![CDATA[Stegeman.]]></given-names>
</name>
</person-group>
<source><![CDATA[Classical Harmonic Analysis and Locally Compact Groups]]></source>
<year>2000</year>
<publisher-loc><![CDATA[Oxford ]]></publisher-loc>
<publisher-name><![CDATA[Clarendon Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[W]]></surname>
<given-names><![CDATA[Rudin.]]></given-names>
</name>
</person-group>
<source><![CDATA[Fourier Analysis on Groups]]></source>
<year>1962</year>
<month>.</month>
<publisher-loc><![CDATA[New York NY ]]></publisher-loc>
<publisher-name><![CDATA[Interscience]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[J]]></surname>
<given-names><![CDATA[Schiff]]></given-names>
</name>
<name>
<surname><![CDATA[S]]></surname>
<given-names><![CDATA[Shnider.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Lie groups and error analysis]]></article-title>
<source><![CDATA[Journal of Lie Theory]]></source>
<year>2001</year>
<volume>11</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>231-254.</page-range></nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[D]]></surname>
<given-names><![CDATA[Sherbert.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Banach algebras of Lipschitz functions]]></article-title>
<source><![CDATA[Pacific J. Math.]]></source>
<year>1963</year>
<volume>13</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>1387-99</page-range></nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[A]]></surname>
<given-names><![CDATA[Ziv.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Relative distance an error measure in round off error analysis]]></article-title>
<source><![CDATA[Math. Comp.]]></source>
<year>1982</year>
<volume>39</volume>
<page-range>563-9</page-range></nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[N]]></surname>
<given-names><![CDATA[Weaver.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Subalgebras of little Lipschitz algebras]]></article-title>
<source><![CDATA[Pacific Journal of Mathematics]]></source>
<year>1996</year>
<volume>173</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>283-93</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
