119 citations · 638 across the 44 of their papers we have counts for
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Difference integrability conditions for parameterized linear difference and differential equations
Alexey Ovchinnikov
This paper is devoted to integrability conditions for systems of linear difference and differential equations with difference parameters. It is shown that such a system is differen…
σ-Galois theory of linear difference equations
Alexey Ovchinnikov, Michael Wibmer
We develop a Galois theory for systems of linear difference equations with an action of an endomorphism σ. This provides a technique to test whether solutions of such systems satis…
Reductive linear differential algebraic groups and the Galois groups of parameterized linear differential equations
Andrey Minchenko, Alexey Ovchinnikov, Michael F. Singer
We develop the representation theory for reductive linear differential algebraic groups (LDAGs). In particular, we exhibit an explicit sharp upper bound for orders of derivatives i…
Unipotent differential algebraic groups as parameterized differential Galois groups
Andrey Minchenko, Alexey Ovchinnikov, Michael F. Singer
We deal with aspects of the direct and inverse problems in parameterized Picard-Vessiot (PPV) theory. It is known that, for certain fields, a linear differential algebraic group (L…