Skip to main content
SpringerLink
Log in

Pictorial Representation for Antisymmetric Eigenfunctions of PS–3 Integral Equations

  • Published:
Mathematical Physics, Analysis and Geometry Aims and scope Submit manuscript

Abstract

Eigenvalue problem for Poincare-Steklov-3 integral equation is reduced to the solution of three transcendential equations for three unknown numbers, moduli of pants. The complete list of antisymmetric eigenfunctions of integral equation in terms of Kleinian membranes is given.

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. Bogatyrev, A.B.: The discrete spectrum of the problem with a pair of Poincare-Steklov operators. Doklady RAS 358(3) (1998)

  2. Bogatyrev, A.B.: The spectral properties of Poincare-Steklov operators. PhD Diss., INM RAS, Moscow (1996)

  3. Bogatyrev, A.B.: A geometric method for solving a series of integral PS equations. Math. Notes 63(3), 302–310 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  4. Poincare, H.: Analyse des travaux scientifiques de Henri Poincare. Acta Math. 38, 3–135 (1921)

    ADS  Google Scholar 

  5. Gunning, R.C.: Special coordinate coverings of Riemann surfaces. Math. Ann. 170, 67–86 (1967)

    Article  MATH  MathSciNet  Google Scholar 

  6. Tyurin, A.N.: On the periods of quadratic differentials. Russ. Math. Surv. 33(6) (1978)

  7. Gallo, D., Kapovich, M., Marden, A.: The monodromy groups of Schwarzian equations on closed Riemann surfaces. Ann. Math. (2) 151(2), 625–704 (2000) See also arXiv, math.CV/9511213

    Article  MATH  MathSciNet  Google Scholar 

  8. Hejhal, D.A.: Monodromy groups and linerly polymorphic functions. Acta Math. 135, 1–55 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  9. Mandelbaum, R.: Branched structures and affine and projective bundles on Riemann surfaces. Trans. AMS 183, 37–58 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  10. Bogatyrev, A.B.: Poincare-Steklov integral equations and the Riemann monodromy problem. Funct. Anal. Appl. 34(2), 9–22 (2000)

    Article  MathSciNet  Google Scholar 

  11. Bogatyrev, A.B.: PS-3 integral equations and projective structures on Riemann surfaces. Sb. Math. 192(4), 479–514 (2001)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Numerical Mathematics, Russian Academy of Sciences, ul. Gubkina 8, 119991, Moscow GSP-1, Russia

    Andrei Borisovich Bogatyrev

Authors
  1. Andrei Borisovich Bogatyrev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Andrei Borisovich Bogatyrev.

Additional information

Supported by RFBR grant 09-01-12160 and RAS Program “Contemporary problems of theoretical mathematics”.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bogatyrev, A.B. Pictorial Representation for Antisymmetric Eigenfunctions of PS–3 Integral Equations. Math Phys Anal Geom 13, 105–143 (2010). https://doi.org/10.1007/s11040-009-9071-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11040-009-9071-1

Keywords

Mathematics Subject Classifications (2000)

Search

Navigation