Skip to main content
SpringerLink
Log in

Analytic extrapolation inL ∞-norm: An alternative approach to “QCD Sum Rules”

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

In view of physical applications (especially to “QCD Sum Rules”), the following problem, pertaining to analytic extrapolation techniques, is studied. We are considering “amplitudes,” which are (real) analytic functions in the complex plane cut alongΓ=[s 0, ∞). A modelF 0(s) of the amplitude is given through the values ofF 0(s) on some intervalγ=[s 2,s 1] (withs 1<s 0) and the values of its discontinuity onΓ. These values are approximate, and are supplemented by prescribed error channels, measured inL ∞-norm (both onΓ andγ). Investigating the compatibility between these data leads to an extremum problem which is solved up to a point where numerical methods can be implemented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Shifman, M. A., Vainshtein, A. I., Zakharov, V. I.: Nucl. Phys.B147, 385, 448 (1979); Bell, J. S., Bertlmann, R. A.: Z. Phys.C4, 11 (1980); Reinders, L. J., Rubinstein, H. R., Yazaki, S.: Phys. Lett.95B, 103 (1980); Yndurain, F. J.: Phys. Lett.63B, 211 (1976); Bertlmann, R. A., Launer, G., De Rafael, E.: Nucl. Phys.B250, 61 (1985); Nasrallah, N. F., Papadopoulos, N. A., Schilcher, K.: Phys. Lett.113B, 61 (1982); Z. Phys.C16, 323 (1983)

    Google Scholar 

  2. Ciulli, M., Ciulli, S., Spearman, T. D.: J. Math. Phys.25, 3194 (1984); Stefanescu, I. S.: J. Math. Phys.27, 2657 (1986)

    Google Scholar 

  3. Auberson, G., Mennessier, G.: Comm. to the Int. Conf. on High Energy Physics, Uppsala 1987; Montpellier preprint PM 87/29

  4. Causse, B., Mennessier, G.: in preparation

  5. Auberson, G. and Ciulli, S.: J. Math. Phys.26, 2737 (1985)

    Google Scholar 

  6. See e.g.: Reed, M., Simon, B.: Methods of modern mathematical physics I: Functional Analysis, Chap. IV. New York, London: Academic Press 1972

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire de Physique Mathématique, U.S.T.L., F-34060, Montpellier Cedex, France

    G. Auberson & G. Mennessier

Authors
  1. G. Auberson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Mennessier
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by H. Araki

Unité Associée au CNRS no040768

Rights and permissions

Reprints and permissions

About this article

Cite this article

Auberson, G., Mennessier, G. Analytic extrapolation inL ∞-norm: An alternative approach to “QCD Sum Rules”. Commun.Math. Phys. 121, 49–62 (1989). https://doi.org/10.1007/BF01218623

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01218623

Keywords

Search

Navigation