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Summary: Solution Spaces of H-Systems and the Ore-Sato Theorem
S. A. Abramov
Russian Academy of Sciences
Dorodnicyn Computing Centre
Vavilova 40, 119991, Moscow GSP-1, Russia
sabramov@ccas.ru
M. Petkovsek
Faculty of Mathematics and Physics
University of Ljubljana,
Jadranska 19, SI-1000 Ljubljana, Slovenia
marko.petkovsek@fmf.uni-lj.si
Abstract
An H-system is a system of first-order linear homogeneous difference equations for a single unknown
function T, with coefficients which are polynomials with complex coefficients. We consider solutions of
H-systems which are of the form T : dom(T) C where either dom(T) = Zd
, or dom(T) = Zd
\ S and
S is the set of integer singularities of the system. It is shown that any natural number is the dimension
of the solution space of some H-system, and that in the case d 2 there are H-systems whose solution
space is infinite-dimensional. The relationships between dimensions of solution spaces in the two cases
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