Spaces of extrafunctions and hypernumbers are special cases of hyperspaces of integral vector spaces. The main constructions are put together in the context of fiber bundles over hyperspaces of integral vector spaces and integral algebras. In this paper, a method of regularization of irregular operations, functionals and operators is developed and applied to multiplication of hypernumbers and extrafunctions (Section 5) and integration of extrafunctions (Sections 6 and 7). Examples of such operations are multiplication, differentiation and integration, which are important for calculus, differential equations and many applications of mathematics, e.g., in physics. However, there are important operations with functions and operators in function spaces the extension of which by coordinates does not work because their application is not invariant with respect to representations of extrafunctions. Examples of such operations are addition of real functions and multiplication of real functions by real numbers. It is proved that it is possible to extend several basic operations with functions and operators in function spaces to regular operations with extrafunctions and operators in spaces of extrafunctions. Operations and operators performed in this manner are called regular. It is possible to perform some operations with extrafunctions and operators in spaces of extrafunctions applying these operations (operators) separately to each coordinate of the representing sequence.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |