NONCOMMUTATIVE JOIN SPACES OF INTEGRAL OPERATORS AND RELATED HYPERSTRUCTURES
Abstract
In this contribution we construct noncommutative transposition hypergroups of integral operators on spaces of continuous functions which are determined by Fredholm integral equations of the first and second kinds. We started with integral operators formed by separated kernel. Moreover, we investigate the obtained hyperstructures as transposition hypergroups and also related quasi-hypergroups of blocks of equivalence of integral operators. Moreover, we use also the object function (where the corresponding binary hyperoperation on an ordered group is defined as principal end generated by products of pairs of elements of the considered group) of a functor enabling the transfer from the category of ordered groups and their isotone homomorphisms into the category of hypergroups and their inclusion homomorphisms.
The basic group of integral operators contains an invariant subgroup. Using another binary operation on the set of suitable Fredholm integral operators of the second kind we get a group with a significant non-invariant subgroup of operators of the first kind enabling the construction of a quasi-hypergroup of decomposition classes of operators, structure of which is also clarified.
The article is a basic analytic material dealing with problems of military techniques maintenance. It analyses current state and assumed development of maintenance of combat, special and transport vehicles, and airplanes in particular NATO countries.
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