On an ad hoc computability structure in a Hilbert space
type: Item
instance of: scholarly article
title: On an ad hoc computability structure in a Hilbert space
zbMATH Open document ID: 1052.03039
author: Atsushi Yoshikawa
published in: Proceedings of the Japan Academy. Series A
publication date: 2004-03-16T00:00:00Z
review text: The author re-examines the ``ad-hoc'' computability structure of \textit{M. B. Pour-El} and \textit{J. I. Richards} [Computability in analysis and physics. Springer-Verlag, Berlin (1989; Zbl 0678.03027)] which was to take an effective generating set as a slightly modified orthonormal basis. He shows that applying the Poincairé-Wigner orthogonalization process to the Pour-El-Richards (loc. cit.) generating set gives an orthonormal effective generating set which yields a third natural computability structure.
reviewed by: Rodney G. Downey
Mathematics Subject Classification ID: 03F60
Mathematics Subject Classification ID: 46S30
Mathematics Subject Classification ID: 03D80
Mathematics Subject Classification ID: 03D45
Mathematics Subject Classification ID: 46C05
zbMATH DE Number: 2058321
zbMATH Keywords: effective generating set
zbMATH Keywords: orthonormal basis
zbMATH Keywords: Poincairé-Wigner orthogonalization
zbMATH Keywords: computability structure
MaRDI profile type: Publication
full work available at URL: pjaa.79.65
OpenAlex ID: W1986418339
cites work: Fractional powers of operators
cites work: Q3994907
DOI: 10.3792/PJAA.79.65
description: scientific article; zbMATH DE number 2058321