Skip to main content
SpringerLink
Log in

Application of the Pontryagin maximum principle to the solution of extremal problems in the class of functions with bounded mean modulus

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

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

Literature Cited

  1. I. I. Privalov, Boundary Properties of Analytic Functions [in Russian], Gostekhizdat, Moscow-Leningrad (1950).

    Google Scholar 

  2. G. M. Goluzin, “Estimates for analytic functions with bounded mean modulus,” Tr. Steklov Mat. Inst., Akad. Nauk SSSR,18, 1–88 (1946).

    Google Scholar 

  3. S. Ya. Khavinson, “On an extremal problem in the theory of analytic functions,” Usp. Mat. Nauk, 4(32), 158–159 (1949).

    Google Scholar 

  4. A. J. Macintyre and W. W. Rogosinski, “Extremum problems in the theory of analytic functions,” Acta Math.,82, 275–325 (1950).

    Google Scholar 

  5. G. Ts. Tumarkin and S. Ya. Khavinson, “Qualitative properties of the solutions of certain types of extremal problems,” in: Investigations of Contemporary Problems in the Theory of Functions of a Complex Variable [in Russian], Fizmatgiz, Moscow (1960), pp. 77–95.

    Google Scholar 

  6. V. Kabaila, “On some interpolation problems in the class Hp for p<1,” Dokl. Akad. Nauk SSSR,132, No. 5, 1002–1004 (1960).

    Google Scholar 

  7. S. A. Gel'fer and L. V. Kresnyakova, “A variational method in the theory of analytic functions with bounded mean modulus,” Mat. Sb.,67, (109), No. 4, 570–585 (1965).

    Google Scholar 

  8. G. M. Goluzin, The Geometric Theory of Functions of a Complex Variable [in Russian], Nauka, Moscow (1966).

    Google Scholar 

  9. V. M. Terpigoreva, “Extremal problems for certain classes of analytic functions with bounded mean modulus,” Dokl. Akad. Nauk SSSR,176, No. 5, 1027–1030 (1967).

    Google Scholar 

  10. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, Mathematical Theory of Optimal Processes [in Russian], Nauka, Moscow (1969).

    Google Scholar 

  11. I. A. Aleksandrov and V. I. Popov, “Optimal control and univalent functions,” Ann. Univ. Marie Curie-Sklodowska Sect. A,24, 13–20 (1970).

    Google Scholar 

  12. I. M. Gal'perin, “Some estimates for functions bounded in the unit disk,” Usp. Mat. Nauk,20, No. 1(121), 197–202 (1965).

    Google Scholar 

  13. R. Nevanlinna, “Überbeschränkte Funktionen, die in gegebenen Punkten vorgeschriebene Werte annehmen,” Ann. Acad. Sci. Fenn. Ser. A,13, No. 1 (1919).

  14. V. P. Vazhdaev and L. V. Kresnyakova, “On analytic functions with bounded mean modulus,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 11 (126), 3–12 (1972).

    Google Scholar 

  15. V. P. Vazhdaev and S. A. Gel'fer, “Some estimates in the class of analytic functions of a bounded form,” Mat. Sb.,84(126), No. 2, 273–289 (1971).

    Google Scholar 

Download references

Authors
  1. V. P. Vazhdaev
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

V. P. Chkalov Institute of Civil Engineering, Gorki. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 21, No. 3, pp. 42–55, May–June, 1980.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vazhdaev, V.P. Application of the Pontryagin maximum principle to the solution of extremal problems in the class of functions with bounded mean modulus. Sib Math J 21, 347–358 (1980). https://doi.org/10.1007/BF00968178

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00968178

Keywords

Search

Navigation