MATHEMATICA BOHEMICA, Vol. 131, No. 2, pp. 197-210 (2006)

Coordinate description of analytic relations

Frantisek Neuman

Frantisek Neuman, Mathematical Institute of the Academy of Sciences, Zizkova 22, CZ-616 62 Brno, Czech Republic, e-mail: neuman@ipm.cz

Abstract: In this paper we present an algebraic approach that describes the structure of analytic objects in a unified manner in the case when their transformations satisfy certain conditions of categorical character. We demonstrate this approach on examples of functional, differential, and functional differential equations.

Keywords: canonical forms, Brandt and Ehresmann groupoids, transformations, differential equations, Abel functional equation, functional differential equations

Classification (MSC2000): 20L05, 34A30, 34C20, 34K05, 39B22, 39B72

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