Skip to main content
Log in

Jessen's theorem for holomorphic almost periodic maps

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

An analog of Jessen's theorem on the existence of a Jessen function and its relation to the distribution of roots of a holomorphic almost periodic function in a strip is obtained for almost periodic maps.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

Literature cited

  1. O. A. Gel'fond, “Roots of systems of almost periodic polynomials,” Preprint No. 78.200, Physics Inst., Acad. Sci. USSR (1978).

  2. O. A. Gel'fond, “Mean index of an almost periodic vector field,” Preprint No. 81.219, Phys. Inst. Acad. Sci. USSR (1981).

  3. A. Hovansky, “Sur les racines complexes des systemes d'equations algebriques ayant en petit monomes,” C.R. Acad. Sci., Paris,191, 937–940 (1981).

    Google Scholar 

  4. A. L. Ronkin, “Distribution of zeros of quasipolynomials of several variables,” Dep. VINITI, No. 375-80, Khar'kov (1980).

  5. A. L. Ronkin, “Distribution of zeros of quasipolynomials of several variables,” Funkts. Anal. Prilozhen.,14, No. 3, 93–94 (1980).

    Google Scholar 

  6. B. Ya. Kazarnovskii, “Zeros of exponential sums,” Dokl. Akad. Nauk SSSR,257, No. 4, 804–806 (1981).

    Google Scholar 

  7. O. A. Gel'fond, Average number of roots of systems of holomorphic almost periodic equations,” Usp. Mat. Nauk,39, No. 1, 123–124 (1984).

    Google Scholar 

  8. L. I. Ronkin, “Jessen's theorem for holomorphic almost periodic equations,” Sib. Mat. Zh.,28, No. 3, 199–204 (1987).

    Google Scholar 

  9. B. Ya. Levin, Distribution of Roots of Entire Functions [in Russian], Gostekhizdat, Moscow (1956).

    Google Scholar 

  10. L. I. Ronkin, “Jessen's theorem for holomorphic almost periodic maps,” Dokl. Akad. Nauk USSR, Ser. A, 10–12 (1957).

  11. P. Lelong and L. Gruman, Entire Functions of Several Complex Variables, Springer-Verlag, New York (1985).

    Google Scholar 

  12. H. Federer, Geometric Measure Theory, Springer-Verlag, New York (1969).

    Google Scholar 

  13. R. Harvey, Holomorphic Chains and Their Boundaries [Russian translation], Nauka, Moscow (1979).

    Google Scholar 

  14. P. Griffiths and J. King, Nevanlinna Theory and Holomorphic Maps of Algebraic Varieties [Russian translation], Mir, Moscow (1976).

    Google Scholar 

  15. L. I. Ronkin, Introduction to the Theory of Entire Functions of Several Variables [in Russian], Nauka, Moscow (1971).

    Google Scholar 

  16. E. M. Chirka, Complex Analytic Sets [in Russian], Nauka, Moscow (1985).

    Google Scholar 

  17. B. V. Shabat, Distribution of Values of Holomorphic Maps [in Russian], Nauka, Moscow (1982).

    Google Scholar 

  18. B. M. Levitan, Almost Periodic Functions [in Russian], Gostekhizdat, Moscow (1953).

    Google Scholar 

  19. C. A. Berenstein and A. Yger, “Ideals generated by exponential polynomials,” Adv. Math.,60, 1–80 (1986).

    Google Scholar 

  20. M. Herve, Functions of Several Complex Variables [Russian translation], Mir, Moscow (1985).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 8, pp. 1094–1107, August, 1990.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ronkin, L.I. Jessen's theorem for holomorphic almost periodic maps. Ukr Math J 42, 976–987 (1990). https://doi.org/10.1007/BF01099231

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01099231

Navigation