JUCS - Journal of Universal Computer Science 16(18): 2523-2534, doi: 10.3217/jucs-016-18-2523
A Constructive Study of Landau's Summability Theorem
Josef Berger‡, Douglas S. Bridges§‡ Mathematisches Institut, Universität München, Germany§ University of Canterbury, Christchurch, New Zealand
Corresponding author: Josef Berger ( josef.berger@mathematik.uni-muenchen.de ) © Josef Berger, Douglas Bridges. This article is freely available under the J.UCS Open Content License. Citation:
Berger J, Bridges DS (2010) A Constructive Study of Landau's Summability Theorem. JUCS - Journal of Universal Computer Science 16(18): 2523-2534. https://doi.org/10.3217/jucs-016-18-2523 |  |
Abstract
A summability theorem of Landau, which classically is a simple consequence of the uniform boundedness theorem, is examined within Bishop-style constructive mathematics. It is shown that the original theorem is nonconstructive, and that a natural weakening of the theorem is constructively equivalent to Ishihara's principle BD-N. The paper ends with a number of results that, while not as strong as Landau's theorem, nevertheless contain positive computational information related to its conclusion.
Keywords
constructive, lp space, summability, Landau