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Conferencias impartidas por Brett Chenoweth

Carleman type theorems in complex analysis and minimal surface theory

Universidad de Liubliana

Carleman’s approximation theorem (1927) was ostensibly the first result concerning approximation of continuous functions defined on an unbounded closed set of C, namely R, by entire functions. The approximation is stronger than uniform approximation as the error at x can be made to taper off as x approaches infinity (from within R). An essential property of R for such an approximation to exist is that it has bounded exhaustion hulls, that is, the complement of R in the one point compactification of C is locally connected at infinity. Bounded exhaustion hulls play an important role in the characterisation of totally real sets admitting Carleman approximation and Carleman approximation of jets; see Manne et al (2011), Magnusson and Wold (2016). In this talk I will discuss some recent generalisations of Carleman’s theorem including preliminary results from ongoing joint work with Ildefonso Castro-Infantes where the problem of approximating by directed holomorphic immersions, for example by null curves, is being considered.

Seminario de la primera planta, IEMath

Brett Chenoweth

Universidad de Liubliana

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Australia

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