Skip to main content
SpringerLink
Log in

On the existence of solutions of synthesis problems for radiating systems in terms of a prescribed amplitude directional pattern

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

We study two variational formulations for nonlinear inverse problems applied to the synthesis of radiating systems, and we derive nonlinear operator equations that follow from the necessary condition for the functional to have a minimum. On the basis of the properties of these functionals we prove theorems and exhibit an existence domain for solutions of this class of problems. Using the example of a linear grid, we exhibit the transition from the variational formulation of a problem to nonlinear integral equations of Hammerstein type.

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

Literature Cited

  1. M. I. Andriichuk and N. N. Voitovich, “Synthesis of a closed planar antenna in terms of a given amplitude directional pattern,”Radiotekh. i Elektron.,30, No. 2, 276–281 (1985).

    Google Scholar 

  2. N. N. Voitovich and P. A. Savenko, “A generalized criterion for nearness of patterns in the problem of synthesizing antennas by the method of V. V. Semenov,”Radiotekh. i Elektron.,18, No. 9, 1794–1798 (1973).

    Google Scholar 

  3. N. N. Voitovich and P. A. Savenko, “Synthesis of antennas from a given amplitude pattern and related problems of quasi-optics (a survey),”Radiotekh. i Elektron.,24, No. 8, 1485–1500 (1979).

    MathSciNet  Google Scholar 

  4. P. P. Zabreiko, A. I. Koshelev, et al.,Integral Equations, [in Russian], Nauka, Moscow (1968).

    Google Scholar 

  5. E. G. Zelkin and V. G. Sokolov,Methods of Synthesizing Antennas [in Russian], Soviet Radio, Moscow (1980).

    Google Scholar 

  6. L. Collatz,Functional Analysis and Numerical Mathematics, Academic Press, New York (1966).

    Google Scholar 

  7. A. N. Kolmogorov and S. V. Fomin,Elements of the Theory of Functions and Functional Analysis, Graylock Press, Rochester (1957).

    Google Scholar 

  8. P. A. Savenko and M. M. Martynyak, “Numerical solution of the problem of synthesizing a spherical antenna grid,”Radiotekh. i Elektron.,32, No. 7, 1539–1542 (1987).

    Google Scholar 

Download references

Authors
  1. P. O. Savenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated fromMatematichni Metody i Fiziko-Mekhanichni Polya, Vol. 38, 1995.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Savenko, P.O. On the existence of solutions of synthesis problems for radiating systems in terms of a prescribed amplitude directional pattern. J Math Sci 81, 3063–3068 (1996). https://doi.org/10.1007/BF02362595

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02362595

Keywords

Search

Navigation