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

This paper introduces the concept of Bessel multipliers. These operators are defined by a fixed multiplication pattern, which is inserted between the analysis and synthesis operators. The proposed concept unifies the approach used for Gabor multipliers for arbitrary analysis/synthesis systems, which form Bessel sequences, like wavelet or irregular Gabor frames. The basic properties of this clas...

In this paper it is investigated how to find a matrix representation of operators on a Hilbert space H with Bessel sequences, frames and Riesz bases. In many applications these sequences are often preferable to orthonormal bases (ONBs). Therefore it is useful to extend the known method of matrix representation by using these sequences instead of ONBs for these application areas. We will give ba...

Communication between natural or artificial agents relies on the use of a common vocabulary. Since sharing terms does not necessarily imply that the terms have exactly the same meanings for all agents, integrating (trigger) statements into a formal ontology requires mechanisms for resolving conflicts that are caused by the ambiguity of terms specified in different but similar ontologies. We def...

BGG sequences on flat homogeneous spaces are analyzed from the point of view of decomposition of appropriate representation spaces on irreducible parts with respect to a maximal compact subgroup, the so called K-types. In particular, the kernels and images of all standard invariant differential operators (including the higher spin analogs of the basic twistor operator), i.e. operators appearing...

We introduce a genuine summation-integral type operators based on Lupaş-Jain base functions related to the unbounded sequences. investigated their degree of approximation in terms modulus continuity and ????-functional for from bounded continuous space. Furthermore, we give some theorems local properties belonging Lipschitz class. Also, Voronovskaja theorem these operators.