Abstract
Integral representations of xk-analytic functions (k=const>0) in terms of boundary values of analytic functions are given. Using these integral representations, three boundary-value problems of xk-analytic functions for a semicircle are solved by quadratures. Bibliography: 4 titles.
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References
G. N. Polzhy,Theory and Application of p-Analytic and (p, q)-Analytic Functions [in Russian], “Naukova dumka”, Kiev (1973).
A. A. Kapshivy, “On the fundamental integral representation ofx-analytic functions and its application to solving some integral equations”,Mat. Fiz., No. 12, 38–46 (1972).
F. D. Gakhov,Boundary Value Problems [in Russian], “Nauka”, Moscow (1977).
A. A. Kapshivy,Methods of Generalized Analytic Functions for Solving Axisymmetric Problems in Elasticity Theory [in Russian], Abstract of doctoral thesis, Tbilisi (1989).
Additional information
Translated fromObchyslyuval’na ta Prykladna Matematyka, No. 76, 1992, pp. 3–12.
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Kapshivy, O.O., Klen, I.V. Solving boundary-value problems ofx k-analytic functions for a semicircle. J Math Sci 75, 1785–1791 (1995). https://doi.org/10.1007/BF02367728
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DOI: https://doi.org/10.1007/BF02367728