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

  • L. P. Castro
  • H. Fujiwara
  • T. Qian
  • S. SaitohEmail author


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.


Reproducing kernel Aveiro discretization Analyticity Numerical experiment Multiplyprecision Band preserving Phase retrieval Sobolev space 



This work was supported in part by Portuguese funds through the CIDMA—Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (FCT), within project PEst-OE/MAT/ UI4106/2014. The fourth named author is supported in part by the Grant-in-Aid for the Scientific Research (C) (2) (No. 24540113).


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • L. P. Castro
    • 1
  • H. Fujiwara
    • 2
  • T. Qian
    • 3
  • S. Saitoh
    • 1
    Email author
  1. 1.CIDMA–Center for Research and Development in Mathematics and Applications, Department of MathematicsUniversity of AveiroAveiroPortugal
  2. 2.Graduate School of InformaticsKyoto UniversityKyotoJapan
  3. 3.Faculty of Science and TechnologyUniversity of MacauTaipaChina

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