Article

    Ufa Mathematical Journal
    Volume 7, Number 3, pp. 3-8

    On the solutions of polynomial growth for a multidimensional generalized Cauchy-Riemann system


    Baizaev S.

    DOI:10.13108/2015-7-3-3

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    Abstact


    For a multidimensional generalized Cauchy-Riemann system we study the Noether property in H\"{o}lder spaces of functions bounded on the whole plane. For the case of constant coefficients we consider the solutions defined on the whole plane or on the half-plane and having a polynomial growth at the infinity. For the two- and three-dimensional cases we find appropriate conditions for the coefficients ensuring that the solutions to the first problem is finite-dimensional or zero or infinite-dimensional, respectively.