Transactions of the Moscow Mathematical Society

This journal, a translation of Trudy Moskovskogo Matematicheskogo Obshchestva, contains the results of original research in pure mathematics.

ISSN 1547-738X (online) ISSN 0077-1554 (print)

The 2024 MCQ for Transactions of the Moscow Mathematical Society is 0.79.

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Best multiband filter problem
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by A. B. Bogatyrev;
Translated by: Christopher Hollings
Trans. Moscow Math. Soc. 2022, 217-225
DOI: https://doi.org/10.1090/mosc/343
Published electronically: September 23, 2024

Abstract:

This mini-review examines the problems of geometric function theory that arise in the synthesis of electric filters, and in particular the work of A. A. Gonchar on the generalisation of Zolotarev’s third problem. The modern development of this topic is described, in particular the method of algebro-geometric Ansatz.
References
  • N. I. Akhiezer, On a problem of E. I. Zolotarev, Izv. AN SSSR. VII Ser. Otdel. Fiz.-Mat. Nauk 2 (1929), 919–931 (in Russian).
  • N. I. Ahiezer, Èlementy teorii èlliptičeskih funkciĭ, Gosudarstv. Izdat. Tehn.-Teor. Lit., Moscow-Leningrad, 1948 (Russian). MR 38492
  • N. I. Akhiezer, Lectures on approximation theory, Nauka, Moscow, 1965 (in Russian).
  • R. A.-R. Amer and H. R. Schwarz, Contributions to the approximation problem of electrical filters, Mitt. Inst. Angew. Math. Zürich 9 (1964), 99. MR 167366
  • A. I. Bobenko and C. Klein, Computational approach to Riemann surfaces, Lecture Notes in Math., 2013, Springer, Heidelberg, 2011.
  • A. B. Bogatyrëv, Èkstremal′nye mnogochleny i rimanovy poverkhnosti, Moskovskiĭ Tsentr Nepreryvnogo Matematicheskogo Obrazovaniya, Moscow, 2005 (Russian, with Russian summary). MR 2287691
  • Andrei B. Bogatyrëv, Computations in moduli spaces, Comput. Methods Funct. Theory 7 (2007), no. 2, 309–324. MR 2376674, DOI 10.1007/BF03321647
  • A. B. Bogatyrëv, Chebyshev representation of rational functions, Mat. Sb. 201 (2010), no. 11, 19–40 (Russian, with Russian summary); English transl., Sb. Math. 201 (2010), no. 11-12, 1579–1598. MR 2768552, DOI 10.1070/SM2010v201n11ABEH004123
  • A. B. Bogatyrëv, Rational functions admitting double decompositions, Trans. Moscow Math. Soc. , posted on (2012), 161–165. MR 3184972, DOI 10.1090/s0077-1554-2013-00207-1
  • Andrei Bogatyrëv, Projective view at optimization problem for multiband filter, Proc. Amer. Math. Soc. 149 (2021), no. 7, 3021–3035. MR 4257812, DOI 10.1090/proc/15452
  • A. B. Bogatyrev, S. A. Goreĭnov, and S. Yu. Lyamaev, Analytical approach to multiband filter synthesis and comparison to other approaches, Problemy Peredachi Informatsii 53 (2017), no. 3, 64–77 (Russian, with Russian summary); English transl., Probl. Inf. Transm. 53 (2017), no. 3, 260–273. MR 3720714, DOI 10.1134/s0032946017030073
  • W. Cauer, Theorie der linearen Wechselstromschaltungen, Bd. 1, Becker & Erler, Leipzig, 1941; Bd. 2, Akademie, Berlin, 1960.
  • V. N. Dubinin, An extremal problem for the derivative of a rational function, Mat. Zametki 100 (2016), no. 5, 732–738 (Russian, with Russian summary); English transl., Math. Notes 100 (2016), no. 5-6, 714–719. MR 3588895, DOI 10.4213/mzm11354
  • V. N. Dubinin, On the logarithmic energy of the zeros and poles of a rational function, Sibirsk. Mat. Zh. 57 (2016), no. 6, 1255–1261 (Russian, with Russian summary); English transl., Sib. Math. J. 57 (2016), no. 6, 981–986. MR 3613997, DOI 10.1134/s0037446616060057
  • W. H. J. Fuchs, On Chebyshev approximation on sets with several components, Aspects of contemporary complex analysis (Proc. NATO Adv. Study Inst., Univ. Durham, Durham, 1979) Academic Press, London-New York, 1980, pp. 399–408. MR 623482
  • G. M. Goluzin, Geometricheskaya teoriya funktsiĭ kompleksnogo peremennogo, 2nd ed., Izdat. “Nauka”, Moscow, 1966 (Russian). Edited by V. I. Smirnov; With a supplement by N. A. Lebedev, G. V. Kuzmina and Ju. E. Alenicyn. MR 219714
  • A. A. Gončar, The problems of E. I. Zolotarev which are connected with rational functions, Mat. Sb. (N.S.) 78(120) (1969), 640–654 (Russian). MR 254238
  • V. I. Lebedev, On finding polynomials of best weighted approximation, Mat. Sb. 199 (2008), no. 2, 49–70 (Russian, with Russian summary); English transl., Sb. Math. 199 (2008), no. 1-2, 207–228. MR 2402198, DOI 10.1070/SM2008v199n02ABEH003916
  • V. Lunot, S. Bila and F. Seyfert, Optimal synthesis for multi-band microwave filters, 2007 IEEE/MTT-S International Microwave Symposium, 2007, pp. 115–118.
  • V. N. Malozëmov, The synthesis problem for a multipole electrical filter, Zh. Vychisl. Mat. i Mat. Fiz. 19 (1979), no. 3, 601–609, 796 (Russian). MR 538929
  • E. Ja. Remez, Osnovy chislennykh metodov chebyshevskogo priblizheniya, “Naukova Dumka”, Kiev, 1969 (Russian). MR 280920
  • E. Stiefel, Le problème d’approximation dans la théorie des filtres électriques, Colloque sur l’analyse numérique à Mons, 1961, pp. 81–87.
  • E. Stiefel, Methods—old and new—for solving the Tchebycheff approximation problem, J. Soc. Indust. Appl. Math. Ser. B Numer. Anal. 1 (1964), 164–176. MR 177501, DOI 10.1137/0701014
  • L. Veidinger, On the numerical determination of the best approximations in the Chebyshev sense, Numer. Math. 2 (1960), 99–105. MR 139889, DOI 10.1007/BF01386215
  • J. L. Walsh, Interpolation and approximation by rational functions in the complex domain, 4th ed., American Mathematical Society Colloquium Publications, Vol. XX, American Mathematical Society, Providence, RI, 1965. MR 218588
  • E. I. Zolotarev, Application of elliptic functions to the problem of functions which vary the least or the most from zero, Zap. Imper. Akad. Nauk 30(5) (1877), 1–71.
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Bibliographic Information
  • A. B. Bogatyrev
  • Affiliation: Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences, Moscow
  • MR Author ID: 337598
  • ORCID: 0000-0002-9581-4554
  • Email: ab.bogatyrev@gmail.com
  • Published electronically: September 23, 2024
  • Additional Notes: The theoretical part of the work was supported by Russian Science Foundation grant 21-11-00325, and the numerical experiments were carried out with the support of the Departments of the Marchuk Institute, Moscow Centre for Fundamental and Applied Mathematics (Agreement 075-15-2022-286)

  • Dedicated: Dedicated to the 90th birthday of Andrey Alexandrovich Gonchar
  • © Copyright 2024 American Mathematical Society
  • Journal: Trans. Moscow Math. Soc. 2022, 217-225
  • MSC (2020): Primary 30E10, 30F30, 30C10
  • DOI: https://doi.org/10.1090/mosc/343