# zbMATH — the first resource for mathematics

Difference equations for functions analytic beyond several squares. (Russian, English) Zbl 1029.30023
Sib. Mat. Zh. 44, No. 3, 550-559 (2003); translation in Sib. Math. J. 44, No. 3, 435-442 (2003).
Summary: We consider some set of squares constructed for the primitive periods 1 and $$i$$ and sufficiently distant from each other. In a neighborhood of this set we study a four-element difference equation with constant coefficients whose linear shifts are generators of the corresponding doubly periodic group and their inverses. A solution is sought in the class of functions analytic beyond this set and vanishing at infinity. We show that the solvability of the problem depends essentially not only on the choice of the coefficients but also on the disposition of the squares.

##### MSC:
 30E25 Boundary value problems in the complex plane 30E20 Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane 39A10 Additive difference equations
Full Text: