arXiv subjects

Sergei Abramov

Publications and source records attributed to Sergei Abramov.

2 recordsLinked to original sources

arXiv2024

On the dimension of the solution space of linear difference equations over the ring of infinite sequences

For a linear difference equation with the coefficients being computable sequences, we establish algorithmic undecidability of the problem of determining the dimension of the solution space including the case when some additional prior information on the dimension is available.

cs.SC↗

arXiv2023

Linear difference operators with sequence coefficients having infinite-dimentional solution spaces

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 infinite numerical sequences, a criterion (i.e., a necessary and sufficient condition) for the infinite dimensionality of its space $V_L$ of solutions belonging to R is the presence of a lacunary sequence in $V_L$.

cs.SC↗