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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2002, Volume 236, Pages 142–152 (Mi tm284)  
This article is cited in 2 scientific papers (total in 2 papers)

On the Boundary Properties of Solutions to the Generalized Cauchy–Riemann Equation

E. P. Dolzhenkoa, V. I. Danchenkob

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Vladimir State University
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Abstract: The paper continues the study of boundary properties of polyanalytic functions and their holomorphic components started by the authors in 1998. Integral formulas for polyanalytic functions and their components as well as some generalizations of the Cauchy integral formula to polyanalytic functions are obtained. For polyanalytic and polyharmonic functions, special mean value theorems and a local maximum principle are proved. Some growth estimates for formal derivatives of polyanalytic (in particular, polyrational) functions and for their components near the boundary of their domain are found. For biharmonic functions, necessary conditions for a local extremum are pointed out.
Received in December 2000
Bibliographic databases:
UDC: 517.53
Language: Russian
Citation: E. P. Dolzhenko, V. I. Danchenko, “On the Boundary Properties of Solutions to the Generalized Cauchy–Riemann Equation”, Differential equations and dynamical systems, Collected papers. Dedicated to the 80th anniversary of academician Evgenii Frolovich Mishchenko, Trudy Mat. Inst. Steklova, 236, Nauka, MAIK «Nauka/Inteperiodika», M., 2002, 142–152; Proc. Steklov Inst. Math., 236 (2002), 132–142
Citation in format AMSBIB
\Bibitem{DolDan02}
\by E.~P.~Dolzhenko, V.~I.~Danchenko
\paper On the Boundary Properties of Solutions to the Generalized Cauchy--Riemann Equation
\inbook Differential equations and dynamical systems
\bookinfo Collected papers. Dedicated to the 80th anniversary of academician Evgenii Frolovich Mishchenko
\serial Trudy Mat. Inst. Steklova
\yr 2002
\vol 236
\pages 142--152
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm284}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=1931014}
\zmath{https://zbmath.org/?q=an:1079.30056}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2002
\vol 236
\pages 132--142
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