5 citations · 6 across the 3 of their papers we have counts for
4 papers
Linear difference operators with sequence coefficients having infinite-dimentional solution spaces
Sergei Abramov, Gleb Pogudin
The notion of lacunary infinite numerical sequence is introduced. It is shown that for an arbitrary linear difference operator L with coefficients belonging to the set R of infinit…
On Rational and Hypergeometric Solutions of Linear Ordinary Difference Equations in -field extensions
Sergei A. Abramov, Manuel Bronstein, Marko Petkovšek +1
We present a complete algorithm that computes all hypergeometric solutions of homogeneous linear difference equations and rational solutions of parameterized linear difference equa…
Convolutions of Liouvillian Sequences
Sergei A. Abramov, Marko Petkovšek, Helena Zakrajšek
While Liouvillian sequences are closed under many operations, simple examples show that they are not closed under convolution, and the same goes for d'Alembertian sequences. Nevert…
Apparent Singularities of Linear Difference Equations with Polynomial Coefficients
S. A. Abramov, M. A. Barkatou, M. van Hoeij
Let L be a linear difference operator with polynomial coefficients. We consider singularities of L that correspond to roots of the trailing (resp. leading) coefficient of L. We pro…