Massaneda Clares, Francesc XavierOrtega Cerdà, JoaquimCruz Rodríguez, Carlos Arturo2017-02-282017-02-282016-06-21https://hdl.handle.net/2445/107528Treballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2016, Director: Francesc Xavier Massaneda Clares i Joaquim Ortega CerdàWe study the discretisation procedure of homogeneous polynomials in the unit sphere $\mathbb{S}\cong \mathbb{CP}^1$. This can be seen as a basic model of a more general problem of discretisation of sections of holomorphic line bundles over compact complex manifolds. Our aim is to obtain geometric necessary and sufficient conditions describing the discretising sequences. An important model for such sequences are the so-called Fekete arrays, which can be seen as nets adapted to the geometry of the sphere. The tools used in such description go back to the signal processing theory pioneered by Beurling and Landau.60 p.application/pdfengcc-by-nc-nd (c) Carlos Arturo Cruz Rodrı́guez, 2016http://creativecommons.org/licenses/by-nc-nd/3.0/es/Funcions de variables complexesTeoria del potencial (Matemàtica)Treballs de fi de màsterEspais funcionalsFunctions of complex variablesPotential theory (Mathematics)Master's thesesFunction spacesinfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/openAccess