ALGEBRAIC EQUATIONS WITH LINEAR SHIFT OPERATORS ON SEQUENCES

Abstract

In this note we recall (see also [8]) the structure of all recurrent sequences which satisfy a fixed recurrence relation, with entries in a perfect field. As a consequence of these considerations we give a reasonable proof for the known result that the Hadamard product of two recurrent sequences is also a recurrent sequence.

Keywords

• recurrent sequence
• shift operator
• algebraic equation
• Hadamard product