How to Catch Smoothing Properties and Analyticity of Functions by Computers?

L. P. Castro (), H. Fujiwara (), T. Qian () and S. Saitoh ()
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L. P. Castro: University of Aveiro, CIDMA–Center for Research and Development in Mathematics and Applications, Department of Mathematics
H. Fujiwara: Kyoto University, Graduate School of Informatics
T. Qian: University of Macau, Faculty of Science and Technology
S. Saitoh: University of Aveiro, CIDMA–Center for Research and Development in Mathematics and Applications, Department of Mathematics

A chapter in Mathematics Without Boundaries, 2014, pp 101-116 from Springer

Abstract: Abstract We would like to propose a new method in view to catch smoothing properties and analyticity of functions by computers. Of course, in the strict sense, such goal is impossible. However, we would like to propose some practical method that may be applied for many concrete cases for some good functions (but not for bad functions, in a sense). Therefore, this may be viewed as a procedure proposal which includes numerical experiments for the just mentioned challenge and within a new method.

Keywords: Reproducing kernel; Aveiro discretization; Analyticity; Numerical experiment; Multiplyprecision; Band preserving; Phase retrieval; Sobolev space (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-1-4939-1124-0_4

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