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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Article on MathNetAbstact
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.