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Discrete Clifford analysis: an overview

dc.creatorBrackx, Fred
dc.creatorDe Schepper, Hennie
dc.creatorSommen, Frank
dc.creatorVan de Voorde, Liesbet
dc.date2009-03-01
dc.date.accessioned2019-05-03T12:36:39Z
dc.date.available2019-05-03T12:36:39Z
dc.identifierhttp://revistas.ufro.cl/ojs/index.php/cubo/article/view/1479
dc.identifier.urihttp://revistaschilenas.uchile.cl/handle/2250/84210
dc.descriptionWe give an account of our current research results in the development of a higher dimensional discrete function theory in a Clifford algebra context. On the simplest of all graphs, the rectangular ℤm grid, the concept of a discrete monogenic function is introduced. To this end new Clifford bases, involving so–called forward and backward basis vectors and introduced by means of their underlying metric, are controlling the support of the involved operators. As our discrete Dirac operator is seen to square up to a mixed discrete Laplacian, the resulting function theory may be interpreted as a refinement of discrete harmonic analysis. After a proper definition of some topological concepts, function theoretic results amongst which Cauchy’s theorem and a Cauchy integral formula are obtained. Finally a first attempt is made at creating a general model for the Clifford bases used, involving geometrically interpretable curvature vectors.en-US
dc.formatapplication/pdf
dc.languageeng
dc.publisherUniversidad de La Frontera. Temuco, Chile.en-US
dc.relationhttp://revistas.ufro.cl/ojs/index.php/cubo/article/view/1479/1333
dc.sourceCUBO, A Mathematical Journal; Vol. 11 Núm. 1 (2009): CUBO, A Mathematical Journal; 55–71es-ES
dc.sourceCUBO, A Mathematical Journal; Vol 11 No 1 (2009): CUBO, A Mathematical Journal; 55–71en-US
dc.source0719-0646
dc.source0716-7776
dc.titleDiscrete Clifford analysis: an overviewen-US
dc.typeinfo:eu-repo/semantics/article
dc.typeinfo:eu-repo/semantics/publishedVersion


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