Multidimensional Riemann-Hilbert type problems in Leibniz algebras with logarithms

• Autorzy: Przeworska-Rolewicz D.
• Języki publikacji: EN

Abstrakty

EN

Riemann-Hilbert type problems in Leibniz algebras with logarithms have been studied in PR[8] (cf. Chapter 14). These problems correspond to such classical problems when the Cauchy transformation is an involution. It was shown that this involution is not multiplicative. On the other hand, in the same book equations with multiplicative involutions were considered. These results can be applied to equations with an involutive transformation of argument, in particular, to equations with transformed argument by means of a function of Carleman type. Riemann-Hilbert type problems with an additional multiplicative involution in commutative Leibniz algebras with logarithms are examined in PR[13]. Results obtained there can be applied not only to problems with a transformation of argument but also to problems with the conjugation (in the complex sense). In the present paper there are considered similar problems in several variables with Riemann- Hilbert condition posed on each variable separately. For instance, these problems correspond in the classical case to problems for polyanalytic functions on polydiscs (cf. HD[1], Ms[1).

Słowa kluczowe

EN

Riemann-Hilbert problem; analytic function; Cauchy singular integral; Leibniz condition; Carleman function; conjugation; logarithmic mapping

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2002
• Tom: Vol. 35, nr 3
• Strony: 629--644
• Opis fizyczny: Bibliogr. 25 poz.

Twórcy

autor

Przeworska-Rolewicz D.

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland

Bibliografia

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