<?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>S1409-24332017000100096</article-id>
<article-id pub-id-type="doi">10.15517/rmta.v24i1.27773</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[On a generalization of the maximum entropy theorem of burg]]></article-title>
<article-title xml:lang="es"><![CDATA[Sobre una generalización de la máxima entropía teorema de burg]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Marcano]]></surname>
<given-names><![CDATA[José]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Infante]]></surname>
<given-names><![CDATA[Saba]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Sánchez]]></surname>
<given-names><![CDATA[Luis]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad de Carabobo  ]]></institution>
<addr-line><![CDATA[ Valencia]]></addr-line>
<country>VE</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad de Carabobo  ]]></institution>
<addr-line><![CDATA[ Valencia]]></addr-line>
<country>VE</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Universidad de Carabobo  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>VE</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2017</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2017</year>
</pub-date>
<volume>24</volume>
<numero>1</numero>
<fpage>96</fpage>
<lpage>113</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S1409-24332017000100096&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S1409-24332017000100096&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S1409-24332017000100096&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[AbstractIn this article we introduce some matrix manipulations that allow us to obtain a version of the original Christoffel-Darboux formula, which is of interest in many applications of linear algebra. Using these developments matrix and Jensen&#8217;s inequality, we obtain the main result of this proposal, which is the generalization of the maximum entropy theorem of Burg for multivariate processes.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[ResumenEn este artículo se introducen algunas manipulaciones matriciales que nos permiten obtener una versión de la fórmula original de ChristoffelDarboux, la cual resulta de interés en muchas aplicaciones del álgebra lineal. Usando estos desarrollos matriciales y la desigualdad de Jensen, se obtiene el resultado principal de esta propuesta, que consiste en la generalización del teorema de entropía máxima de Burg para procesos multivariados.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[multivariate processes]]></kwd>
<kwd lng="en"><![CDATA[maximum entropy theorem]]></kwd>
<kwd lng="en"><![CDATA[Christoffel-Darboux formula]]></kwd>
<kwd lng="es"><![CDATA[procesos multivariados]]></kwd>
<kwd lng="es"><![CDATA[teorema de entropía máxima]]></kwd>
<kwd lng="es"><![CDATA[fórmula de Christoffel-Darboux]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Problem of search of the minimun of entropy in indeterminate extension problems]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Arov]]></surname>
<given-names><![CDATA[D.Z.]]></given-names>
</name>
<name>
<surname><![CDATA[Krein]]></surname>
<given-names><![CDATA[M.G.]]></given-names>
</name>
</person-group>
<source><![CDATA[Funt. Anal. Appl.]]></source>
<year>1981</year>
<volume>15</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>123-6</page-range></nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Burg]]></surname>
<given-names><![CDATA[J.P.]]></given-names>
</name>
</person-group>
<source><![CDATA[Maximum Entropy Spectral Analysis]]></source>
<year>1975</year>
<publisher-loc><![CDATA[Stanford, California ]]></publisher-loc>
<publisher-name><![CDATA[Stanford University]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Choi]]></surname>
<given-names><![CDATA[B.S.]]></given-names>
</name>
</person-group>
<source><![CDATA[On the relation bemtween the maximum entropy probability density function and the autoregressive model]]></source>
<year>1986</year>
</nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Multivariate maximum entropy spectrum]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Choi]]></surname>
<given-names><![CDATA[B.S.]]></given-names>
</name>
</person-group>
<source><![CDATA[J. Multivariate Anal]]></source>
<year>1993</year>
<volume>46</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>56-60</page-range></nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Orthogonal polynomial matrices on the unit circles]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Delsarte]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Genin]]></surname>
<given-names><![CDATA[Y.]]></given-names>
</name>
<name>
<surname><![CDATA[Kamp]]></surname>
<given-names><![CDATA[Y.]]></given-names>
</name>
</person-group>
<source><![CDATA[IEEE Trans. Circuits Syst.]]></source>
<year>1978</year>
<volume>25</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>149-60</page-range></nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Dym]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
</person-group>
<source><![CDATA[J. contractive matrix function, reproducing kernel Hilbert spaces and interpolation]]></source>
<year>1989</year>
<publisher-loc><![CDATA[Providence, RI ]]></publisher-loc>
<publisher-name><![CDATA[A.M.S.]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Extension of positive definite distributions and maximum entropy]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Gabardo]]></surname>
<given-names><![CDATA[J.P.]]></given-names>
</name>
</person-group>
<source><![CDATA[Mem. Am. Math. Soc.]]></source>
<year>1993</year>
<volume>102</volume>
<numero>489</numero>
<issue>489</issue>
</nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Maximum entropy and the moment problem]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Landau]]></surname>
<given-names><![CDATA[H.J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Bull. Am. Math. Soc]]></source>
<year>1987</year>
<volume>16</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>47-77</page-range></nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[The Arov-Grossman model and Burg multivariate entropy]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Marcano]]></surname>
<given-names><![CDATA[J.G.]]></given-names>
</name>
<name>
<surname><![CDATA[Moran]]></surname>
<given-names><![CDATA[M.D.]]></given-names>
</name>
</person-group>
<source><![CDATA[J. Fourier Anal. Appl.]]></source>
<year>2003</year>
<volume>9</volume>
<numero>6</numero>
<issue>6</issue>
<page-range>623-47</page-range></nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Marcano]]></surname>
<given-names><![CDATA[J.G.]]></given-names>
</name>
<name>
<surname><![CDATA[Moran]]></surname>
<given-names><![CDATA[M.D.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The Arov-Grossman model and Burg&#8217;s entropy]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Baez-Yates]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Glaz]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Gzyl]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
<name>
<surname><![CDATA[Hüsler]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Palacios]]></surname>
<given-names><![CDATA[J.L.]]></given-names>
</name>
</person-group>
<source><![CDATA[Recent Adv. Appl. Probab.]]></source>
<year>2005</year>
<page-range>329-64</page-range><publisher-loc><![CDATA[Boston ]]></publisher-loc>
<publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Masani]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Recent trends in multivariate prediction theory]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Krishnaiah]]></surname>
<given-names><![CDATA[P.R.]]></given-names>
</name>
</person-group>
<source><![CDATA[Multivariate Analysis]]></source>
<year>1966</year>
<page-range>351- 382</page-range><publisher-loc><![CDATA[New York ]]></publisher-loc>
<publisher-name><![CDATA[Academic Press]]></publisher-name>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
