<?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>1405-7743</journal-id>
<journal-title><![CDATA[Ingeniería, investigación y tecnología]]></journal-title>
<abbrev-journal-title><![CDATA[Ing. invest. y tecnol.]]></abbrev-journal-title>
<issn>1405-7743</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional Autónoma de México, Facultad de Ingeniería]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1405-77432005000100001</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[&#8220;A Tensorial Form of the Theory of Functions&#8221;. An Engineering Application to: Polynomial Interpolation]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Urrutia-Galicia]]></surname>
<given-names><![CDATA[J.L.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,UNAM Instituto de Ingeniería Coordinación de Mecánica Aplicada]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>03</month>
<year>2005</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>03</month>
<year>2005</year>
</pub-date>
<volume>6</volume>
<numero>1</numero>
<fpage>1</fpage>
<lpage>11</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S1405-77432005000100001&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S1405-77432005000100001&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S1405-77432005000100001&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract From basic concepts such as: tensor calculus (Flügge, 1972); functional analysis (Mikhlin, 1964) and solid mechanics (Soedel, 1972) the objective of y his objetive is to show that besides the &#8220;n&#8221; covariant functions (of functional analysis), linearly independent and not necessarily orthogonal, there is another group of &#8220;n&#8221; contravariant functions that are biorthogonal to the former group. The presentation of these two families gives rise to a new formulation of functional analysis in skew coordinates. We will see that the concept of skew manifolds finds immediate applicability to the problem of interpolation of arbitrary functions via the use of the new concept of covariant and contravariant polynomials. The theory and the examples demonstrate that the problems of interpolation and Fourier analysis can be grouped into one single theory.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen A partir de conceptos básicos de cálculo tensorial (Flügge, 1972), análisis funcional (Mikhlin, 1964) y de mecánica de sólidos (Soedel, 1972), el objetivo de este artículo es demostrar que además de las &#8220;n&#8221; funciones covariantes (de análisis funcional), linealmente independientes pero no necesariamente ortogonales, existe otro grupo de &#8220;n&#8221; funciones contravariantes que son biortogonales al grupo anterior. La presentación de estas dos familias de funciones da origen a una nueva formulación de análisis funcional en coordenadas oblicuas. Veremos que el concepto de espacios coordenados oblicuos encuentra aplicación inmediata al problema de interpolación de funciones arbitrarias vía el uso del nuevo concepto de polinomios covariantes y contravariantes. La teoría y los ejemplos demuestran que los problemas de interpolación y análisis de Fourier se pueden agrupar y tratar dentro de una sola y única teoría.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Interpolation]]></kwd>
<kwd lng="en"><![CDATA[index notation]]></kwd>
<kwd lng="en"><![CDATA[covariant and contravariant polynomials]]></kwd>
<kwd lng="en"><![CDATA[general skew manifolds (Tensor calculus)]]></kwd>
<kwd lng="en"><![CDATA[tensorial theory of functions]]></kwd>
<kwd lng="en"><![CDATA[convergence]]></kwd>
<kwd lng="es"><![CDATA[Interpolación]]></kwd>
<kwd lng="es"><![CDATA[notación índice]]></kwd>
<kwd lng="es"><![CDATA[polinomios covariantes y contravariantes]]></kwd>
<kwd lng="es"><![CDATA[espacios generales oblicuos (cálculo tensorial)]]></kwd>
<kwd lng="es"><![CDATA[teoría tensorial de funciones]]></kwd>
<kwd lng="es"><![CDATA[convergencia]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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