On integration and differentiation of generalized analytic functions
Titel:
On integration and differentiation of generalized analytic functions
Auteur:
Tutschke, W. Withalm, C.
Verschenen in:
Complex variables and elliptic equations
Paginering:
Jaargang 29 (1996) nr. 4 pagina's 319-332
Jaar:
1996-05
Inhoud:
As it is well-known, the complex differentiation of a holomorphic function can be inverted by a complex line integral not depending on the path of integration locally, at least. In the present paper inverse integral operators to more general first order operators (containing a partial complex derivative) are constructed. The construction is based on the concept of associated differential operators. L. Bers' (F,G)-derivative can be interpreted as a special associated differential operator (to the corresponding elliptic first order system) in case the (F,G)-derivative of an (F,G)-pseudo-analytic function is (F,G)-pseudo-analytic again. On the other hand, there are elliptic first order systems having associated operators but not having an (F,G)-pseudo-analytic (F,G)-derivative (cf. Section 2.3). The main result of the present paper is a Volterra integral equation whose solutions define the inverse operator to the associated differential operator. That way one gets generalizations of Cauchy's integral theorem and of the Morera theorem as well.
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