Abstract
A general approach is proposed to the interpolation of x α -analytical functions of a complex variable with an arbitrary α ε−∞,+∞[Basis x α -analytical functions whose imaginary pan is a polynomial in x, and y are obtained in explicit form.
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A. A. Klunnik and V. L. Makarov, “On convergence of the interpolation process in the class ofx α-analytical functions of a complex variable,” Ukr. Mat. Zh.,35, No. 2, 151–155 (1983).
A. A. Klunnik and V. L. Makarov, “On existence and uniqueness of an x2k-analytical interpolation function of a complex variable,” Vychisl. Prikl. Mat., No. 46, 43–54 (1982).
V. L. Makarov, A. A. Klunnik, and N. P. Kopystra, “On uniqueness of x2-analytical interpolation function of a complex variable,” Vychisl. Prikl. Mat., No. 44, 89–98 (1981).
V. L. Makarov, A. A. Klunnik, and N. P. Kopystra, “Some issues of interpolation of xα-analytical functions of a complex variable,” Vychisl. Prikl. Mat., No. 42, 132–137 (1980).
G. N. Polozhii, Theory and Application of p-Analytical and (p, q)-Analytical Functions [in Russian], Naukova Dumka, Kiev (1972).
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Translated from Vychislitel'naya i Prikladnaya Matematika, No. 58, pp. 3–9, 1986.
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Klunnik, A.A. Interpolation of generalized analytical functions of complex variable. J Math Sci 58, 391–395 (1992). https://doi.org/10.1007/BF01100061
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DOI: https://doi.org/10.1007/BF01100061