On an ad hoc computability structure in a Hilbert space. (English) Zbl 1052.03039

The author re-examines the “ad-hoc” computability structure of M. B. Pour-El and 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.


03F60 Constructive and recursive analysis
46S30 Constructive functional analysis
03D80 Applications of computability and recursion theory
03D45 Theory of numerations, effectively presented structures
46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)


Zbl 0678.03027
Full Text: DOI


[1] Daubechies, I.: Ten Lectures on Wavelets (CBMS-NSF Regional Conference Series in Applied Mathematics, no.,61). Society for Industrial and Applied Mathematics (SIAM), Philadelphia (1992).
[2] Komatsu, H.: Fractional powers of operators. Pacific J. Math., 19 , 285-346 (1966). · Zbl 0154.16104 · doi:10.2140/pjm.1966.19.285
[3] Pour-El, Marian B., and Richards, J. Ian: Computability in Analysis and Physics. Springer-Verlag, Berline-Heidelberg (1989). · Zbl 0678.03027
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