Geodesic
Fejer radiation pattern for linear antenna and solving the problem of amplitude-phase synthesis
Čelâbinskij fiziko-matematičeskij žurnal, Tome 5 (2020) no. 2, pp. 211-217.

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For the first time, the problem of amplitude-phase synthesis for a linear antenna with a radiation pattern represented by the Fejer core is solved. It turns out that the design of such radiation patterns combines both the interpolation capabilities of Hermite polynomials used for this purpose in the works of P.K. Suetin and the approximation properties of trigonometric sums, which are Fourier transforms of atomic functions indicated in B.F. Kravchenko.
Keywords: Fejer sum, orthogonal polynomial, radiation pattern, linear antenna, problem of amplitude-phase synthesis. 
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V. A. Kostin; D. V. Kostin; A. V. Kostin. Fejer radiation pattern for linear antenna and solving the problem of amplitude-phase synthesis. Čelâbinskij fiziko-matematičeskij žurnal, Tome 5 (2020) no. 2, pp. 211-217. http://geodesic.mathdoc.fr/item/CHFMJ_2020_5_2_a1/

[1] Suetin P.K., The beginning of the mathematical theory of antennas, Insvyaz' Publ., Moscow, 2008, 228 pp. (In Russ.)

[2] Suetin P.K., Classical orthogonal polynomials, Nauka Publ., Moscow, 1979, 416 pp. (In Russ.)

[3] Kravchenko V.F., Lectures on the theory of atomic functions and some of their applications, Radiotekhnika Publ., Moscow, 2003, 512 pp. (In Russ.)

[4] Kostin V.A., Kostin V.A., Sapronov Yu.I., “Maxwell — Fejer polynomials and optimization of polyharmonic impulse”, Doklady Mathematics, 86:1 (2012), 512–514 | MR | Zbl

[5] Levitan B.M., Almost periodic functions, Gosteortekhizdat Publ., Moscow, 1953, 396 pp. (In Russ.) | MR

[6] Achiezer N.I., Theory of approximation, Frederick Ungar Publ., New York, 623 pp. | MR | MR

[7] Pashkovsky S.P., Computational applications of Chebyshyov polynomials and series, Nauka Publ., Moscow, 1983, 384 pp. (In Russ.) | MR