<?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>S1409-24332015000100003</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Cálculo de coeficientes de fourier en dos variables, una versión distribucional]]></article-title>
<article-title xml:lang="en"><![CDATA[Fourier coefficientes computation in two variables, a distributional version]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Ulate R.]]></surname>
<given-names><![CDATA[Carlos Manuel]]></given-names>
</name>
<xref ref-type="aff" rid="A01"/>
</contrib>
</contrib-group>
<aff id="A01">
<institution><![CDATA[,Universidad de Costa Rica Sede de Occidente ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2015</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2015</year>
</pub-date>
<volume>22</volume>
<numero>1</numero>
<fpage>49</fpage>
<lpage>59</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S1409-24332015000100003&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S1409-24332015000100003&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S1409-24332015000100003&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[En el presente artículo, a partir de la fórmula distribucional de sumación del tipo de Euler-Maclaurin y una adecuada elección de la distribución, se obtienen representaciones para los coeficientes de Fourier en dos variables. Estas representaciones pueden ser usadas para la evaluación numérica de los coeficientes.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[The present article, by considering the distributional summations of Euler-Maclaurin and a suitable choice of the distribution, results in representations for the Fourier coefficients in two variables are obtained. These representations may be used for the numerical evaluation of coefficients.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Sumas Euler-Maclaurin]]></kwd>
<kwd lng="es"><![CDATA[coeficientes de Fourier]]></kwd>
<kwd lng="es"><![CDATA[distribuciones]]></kwd>
<kwd lng="en"><![CDATA[Euler-Maclaurin sums]]></kwd>
<kwd lng="en"><![CDATA[Fourier coefficients]]></kwd>
<kwd lng="en"><![CDATA[distributions]]></kwd>
</kwd-group>
</article-meta>
</front><body><![CDATA[ <div style="text-align: justify;">     <div style="text-align: center;"><font  style="font-family: Verdana; font-weight: bold;" size="4"> C&aacute;lculo de coeficientes de fourier en dos variables, una versi&oacute;n distribucional</font>    <br> <font style="font-family: Verdana;" size="2"></font>    <br> <font style="font-family: Verdana; font-weight: bold;" size="4">Fourier coefficientes computation in two variables, a distributional version</font><font  style="font-family: Verdana; font-weight: bold;" size="3"> </font></div>     <br>     <div style="text-align: center;"><font style="font-family: Verdana;"  size="2">Carlos Manuel Ulate R.<a href="#1">*</a><a name="2"></a>+</font>    <br> </div> <font style="font-family: Verdana;" size="2"></font> <hr style="width: 100%; height: 2px;"><font  style="font-family: Verdana;" size="2"></font><font  style="font-family: Verdana; font-weight: bold;" size="3">Resumen</font>    <br> <font style="font-family: Verdana;" size="2"></font>    <br> <font style="font-family: Verdana;" size="2">En el presente art&iacute;culo, a partir de la f&oacute;rmula distribucional de sumaci&oacute;n del tipo de Euler-Maclaurin y una adecuada elecci&oacute;n de la distribuci&oacute;n, se obtienen representaciones para los coeficientes de Fourier en dos variables. Estas representaciones pueden ser usadas para la evaluaci&oacute;n num&eacute;rica de los coeficientes.</font>    <br> <font style="font-family: Verdana;" size="2"></font>    ]]></body>
<body><![CDATA[<br> <font style="font-family: Verdana;" size="2"><span  style="font-weight: bold;">Palabras clave</span>: Sumas Euler-Maclaurin; coeficientes de Fourier; distribuciones.</font>    <br> <font style="font-family: Verdana;" size="2"></font>    <br> <font style="font-family: Verdana; font-weight: bold;" size="3">Abstract</font>    <br> <font style="font-family: Verdana;" size="2"></font>    <br> <font style="font-family: Verdana;" size="2">The present article, by considering the distributional summations of Euler-Maclaurin and a suitable choice of the distribution, results in representations for the Fourier coefficients in two variables are obtained. These representations may be used for the numerical evaluation of coefficients. </font>    <br> <font style="font-family: Verdana;" size="2"></font>    <br> <font style="font-family: Verdana;" size="2"><span  style="font-weight: bold;">Keywords</span>: Euler-Maclaurin sums, Fourier coefficients, distributions.</font>    <br> <font style="font-family: Verdana;" size="2"></font>    <br> <font style="font-family: Verdana; font-weight: bold;" size="2">Mathematics Subject Classification: 40G05, 42A16.</font>    <br> <hr style="width: 100%; height: 2px;"><font  style="font-family: Verdana;" size="2"></font>    ]]></body>
<body><![CDATA[<br> <font style="font-family: Verdana;" size="2">Ver contenido en pdf.</font>    <br> <font style="font-family: Verdana;" size="2"></font> <hr style="width: 100%; height: 2px;">    <br> <font style="font-family: Verdana; font-weight: bold;" size="3">Referencias</font>    <br> <font style="font-family: Verdana;" size="2"></font>    <br>     <!-- ref --><div style="text-align: left;"><font style="font-family: Verdana;"  size="2">[1] Estrada, R.; Kanwal R.P. (1994) <span  style="font-style: italic;">Asymptotic Analysis: A Distributional Approach</span>. Birkh&auml;user, Boston.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=1941300&pid=S1409-2433201500010000300001&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font>    <br>     <!-- ref --><br> <font style="font-family: Verdana;" size="2">[2] Kanwal, R.P. (1997) <span  style="font-style: italic;">Generalized Functions: Theory and Technique</span>, 2a edici&oacute;n. Birkh&auml;user, Boston.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=1941303&pid=S1409-2433201500010000300002&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font>    ]]></body>
<body><![CDATA[<br>     <!-- ref --><br> <font style="font-family: Verdana;" size="2">[3] Lyness, J. N. (1970) &#8220;The calculation of Fourier coefficients by the M&ouml;bius inversion of the Poisson summation formula, Part I. Functions whose early derivatives are continuous&#8221;,<span  style="font-style: italic;"> Math. of Comp</span>.<span  style="font-weight: bold;"> 24</span>: 101&#8211;135.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=1941306&pid=S1409-2433201500010000300003&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font>    <br>     <!-- ref --><br> <font style="font-family: Verdana;" size="2">[4] Schwartz, L. (1966) <span  style="font-style: italic;">Th&eacute;orie des Distributions</span>. Hermann, Paris.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=1941309&pid=S1409-2433201500010000300004&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font>    <br>     <!-- ref --><br> <font style="font-family: Verdana;" size="2">[5] Ulate, C.M.; Estrada, R. (1998) &#8220;Una f&oacute;rmula distribucional de sumaci&oacute;n del tipo de Euler-Maclaurin en dos variables&#8221;, <span  style="font-style: italic;">Divulgaciones Matem&aacute;ticas</span><span style="font-weight: bold;"> </span>6: 93&#8211;112.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=1941312&pid=S1409-2433201500010000300005&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font>    <br> </div> <font style="font-family: Verdana;" size="2"></font>    ]]></body>
<body><![CDATA[<br> <font style="font-family: Verdana;" size="2"><a name="1"></a><a  href="#2">*</a> Sede de Occidente, Universidad de Costa Rica, San Ram&oacute;n, Costa Rica. E-Mail: carlos.ulate@ucr.ac.cr</font>    <br> <hr style="width: 100%; height: 2px;"><font  style="font-family: Verdana;" size="2"></font>     <div style="text-align: center;"><font  style="font-family: Verdana; font-weight: bold;" size="2">Received: 15/Feb/2012; Revised: 3/Sep/2014;Accepted: 17/Oct/2014 </font></div> </div>      ]]></body><back>
<ref-list>
<ref id="B1">
<label>1</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Estrada]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Kanwal]]></surname>
<given-names><![CDATA[R.P.]]></given-names>
</name>
</person-group>
<source><![CDATA[Asymptotic Analysis: A Distributional Approach]]></source>
<year>1994</year>
<publisher-loc><![CDATA[^eBoston Boston]]></publisher-loc>
<publisher-name><![CDATA[Birkhäuser]]></publisher-name>
</nlm-citation>
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<name>
<surname><![CDATA[Kanwal]]></surname>
<given-names><![CDATA[R.P.]]></given-names>
</name>
</person-group>
<source><![CDATA[Generalized Functions: Theory and Technique]]></source>
<year>1997</year>
<edition>2</edition>
<publisher-loc><![CDATA[^eBoston Boston]]></publisher-loc>
<publisher-name><![CDATA[Birkhäuser]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B3">
<label>3</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lyness]]></surname>
<given-names><![CDATA[J. N.]]></given-names>
</name>
</person-group>
<article-title xml:lang="en"><![CDATA[“The calculation of Fourier coefficients by the Möbius inversion of the Poisson summation formula, Part I: Functions whose early derivatives are continuous”]]></article-title>
<source><![CDATA[Math. of Comp]]></source>
<year>1970</year>
<volume>24</volume>
<page-range>101-135</page-range></nlm-citation>
</ref>
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<label>4</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Schwartz]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<source><![CDATA[Théorie des Distributions]]></source>
<year>1966</year>
<publisher-loc><![CDATA[^eParis Paris]]></publisher-loc>
<publisher-name><![CDATA[Hermann]]></publisher-name>
</nlm-citation>
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<label>5</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ulate]]></surname>
<given-names><![CDATA[C.M.]]></given-names>
</name>
<name>
<surname><![CDATA[Estrada]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<article-title xml:lang="en"><![CDATA[“Una fórmula distribucional de sumación del tipo de Euler-Maclaurin en dos variables”]]></article-title>
<source><![CDATA[Divulgaciones Matemáticas]]></source>
<year>1998</year>
<volume>6</volume>
<page-range>93-112</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
