Abstract
We present results concerning analytic machines, a model of real computation introduced by Hotz which extends the well known Blum, Shub and Smale machines by infinite converging computations. We use the machine model to define computability of complex analytic (i.e. holomorphic) functions and examine in particular the class of analytic functions which have analytically computable power series expansions. We show that this class is closed under the basic analytic operations composition, local inversion and analytic continuation.
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Gärtner, T., Hotz, G. (2009). Computability of Analytic Functions with Analytic Machines. In: Ambos-Spies, K., Löwe, B., Merkle, W. (eds) Mathematical Theory and Computational Practice. CiE 2009. Lecture Notes in Computer Science, vol 5635. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03073-4_26
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DOI: https://doi.org/10.1007/978-3-642-03073-4_26
Publisher Name: Springer, Berlin, Heidelberg
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