Geodesic
Residues and Argument Principle for $A(z)$-Analytic Functions
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Problems of Modern Topology and its Applications», Tome 144 (2018), pp. 56-64.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we obtain formulas for residues and prove analogs of the argument principle and Rouche theorems for $A(z)$-analytic functions.
Keywords: $A(z)$-analytic function, $A(z)$-lemniscate.
Mots-clés : Cauchy-type kernel 
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Zh. K. Tishabaev; T. U. Otaboev; Sh. Ya. Khursanov. Residues and Argument Principle for $A(z)$-Analytic Functions. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Problems of Modern Topology and its Applications», Tome 144 (2018), pp. 56-64. http://geodesic.mathdoc.fr/item/INTO_2018_144_a5/

[1] Bukhgeim A. L, Formuly obrascheniya v obratnykh zadachakh, Nauka, M., 1991 | MR

[2] Bukhgeim A. L., Kazantsev S. G., “Ellipticheskie sistemy tipa Beltrami i zadachi tomografii”, Dokl. AN SSSR, 315:1 (1990), 15–19

[3] Vekua I. N., Obobschennye analiticheskie funktsii, Nauka, M., 1988

[4] Zhabborov N. M., Imomnazarov Kh. Kh., Nekotorye nachalno-kraevye zadachi mekhaniki dvukhskorostnykh sred, Izd-vo NUUz im. M. Ulugbeka, Tashkent, 2012

[5] Zhabborov N. M., Otaboev T. U., “Teorema Koshi dlya $A(z)$-analiticheskikh funktsii”, Uzbek. mat. zh., 2014, no. 1, 15–18 | MR

[6] Zhabborov N. M., Otaboev T. U., “Analog integralnoi formuly Koshi dlya $A$-analiticheskikh funktsii”, Uzbek. mat. zh., 2016, no. 4, 50–59 | MR

[7] Lavrentev M. A., Shabat B. V., Metody teorii funktsii kompleksnogo peremennogo, Fizmatgiz, M., 1958 | MR

[8] Ahlfors L., Lectures on quasiconformal mappings, Van Nostrand, New York, 1966 | MR | Zbl

[9] Gutlyanski V., Ryazanov V., Srebro U., Yakubov E., The Beltrami equation: A geometric approach, Springer-Verlag, 2011 | MR

[10] Sadullaev A., Jabborov N. M., “On a class of $A$-analytic functions”, J. Sib. Federal Univ. Math. Phys., 3:9 (2016), 374–383 | DOI | MR