The theory of integral equations dipole antennas in the works of P. L. Kapitsa, V. A. Fock and L. A. Weinstein
https://doi.org/10.34680/2076-8052.2025.1(139).151-162
Abstract
The review of the works of P. L. Kapitsa, V. A. Fock and L. A. Weinstein on the theory of integral equations of dipole antennas published in the period from 1959 to 1967 is given. The most significant results are noted, which are still relevant at the present time. The connections between the individual results are emphasized, and the outline of the theory of the kernel of the integral equation is outlined. This theory includes the decomposition of the kernel into a series by products of the Hankel and Bessel functions of the half-integer index, as well as the representation of the kernel through a hypergeometric function. The analysis of the computational experiment of V. A. Fock and L. A. Weinstein for a transmitting dipole was carried out, and a phenomenal coincidence with the results of other methods for solving integral equations with an exact singular kernel was obtained. A theoretical justification of this phenomenon is given.
About the Authors
S. I. Eminov
Yaroslav-the-Wise Novgorod State University
Russian Federation
Russian Federation
Veliky Novgorod
A. V. Sochilin
Yaroslav-the-Wise Novgorod State University
Russian Federation
Russian Federation
Veliky Novgorod
References
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Review
For citations:
Eminov S.I., Sochilin A.V. The theory of integral equations dipole antennas in the works of P. L. Kapitsa, V. A. Fock and L. A. Weinstein. Title in english. 2025;(1(139)):151-162. (In Russ.) https://doi.org/10.34680/2076-8052.2025.1(139).151-162
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