Sequences of Groups, Hypergroups and Automata of Linear Ordinary Differential Operators

The main objective of our paper is to focus on the study of sequences (finite or countable) of groups and hypergroups of linear differential operators of decreasing orders. By using a suitable ordering or preordering of groups linear differential operators we construct hypercompositional structures of linear differential operators. Moreover, we construct actions of groups of differential operators on rings of polynomials of one real variable including diagrams of actions–considered as special automata. Finally, we obtain sequences of hypergroups and automata. The examples, we choose to explain our theoretical results with, fall within the theory of artificial neurons and infinite cyclic groups.

ESSENTIAL SPECTRA OF ORDINARY DIFFERENTIAL OPERATORS II. STABILITY OF SPECTRA

The article contains precise formulas for finding of the essential spectra that are revolted with asymptotically constants on infinity in coefficients with use of rather compact and rather small indignations on infinity in Lebesgue spaces of 𝐿 𝑝 . These formulas are new analogs of the classical theorem of Weyl.