The concept of para-product operators over locally compact Vilenkin groups is established and the applications to the para-linearization in nonlinear problems are studied. This kind of operators plays a special role i...The concept of para-product operators over locally compact Vilenkin groups is established and the applications to the para-linearization in nonlinear problems are studied. This kind of operators plays a special role in dealing with those functions which do not have the classical derivatives.展开更多
Category is put to work in the non-associative realm in the article.We focus on atypical example of non-associative category.Its objects are octonionic bimodules,morphisms are octonionic para-linear maps,and compositi...Category is put to work in the non-associative realm in the article.We focus on atypical example of non-associative category.Its objects are octonionic bimodules,morphisms are octonionic para-linear maps,and compositions are non-associative in general.The octonionic para-linear map is the main object of octonionic Hilbert theory because of the octonionic Riesz representation theorem.An octonionic para-linear map f is in general not octonionic linear since it subjects to the rule Re(f(px)-pf(x))=0.The composition should be modified as f◎g(x):=f(g(x))-7∑j=1ejRe(f(g(e_(i)x))-f(e_(i)g(x)))j=1 so that it preserves the octonionic para-linearity.In this non-associative category,we introduce the Hom and Tensor functors which constitute an adjoint pair.We establish the Yoneda lemma in terms of the new notion of weak functor.To define the exactness in a non-associative category,we introduce the notion of the enveloping category via a universal property.This allows us to establish the exactness of the Hom functor and Tensor functor.展开更多
The concept of para-differential operators over locally compact Vilenkin groups is given and their properties are studied. By means of para-linearization theorem, efforts are made to establish the basic theory of Gibb...The concept of para-differential operators over locally compact Vilenkin groups is given and their properties are studied. By means of para-linearization theorem, efforts are made to establish the basic theory of Gibbs-Butzer differential operators.展开更多
基金the National Natural Science Foundation of China
文摘The concept of para-product operators over locally compact Vilenkin groups is established and the applications to the para-linearization in nonlinear problems are studied. This kind of operators plays a special role in dealing with those functions which do not have the classical derivatives.
文摘Category is put to work in the non-associative realm in the article.We focus on atypical example of non-associative category.Its objects are octonionic bimodules,morphisms are octonionic para-linear maps,and compositions are non-associative in general.The octonionic para-linear map is the main object of octonionic Hilbert theory because of the octonionic Riesz representation theorem.An octonionic para-linear map f is in general not octonionic linear since it subjects to the rule Re(f(px)-pf(x))=0.The composition should be modified as f◎g(x):=f(g(x))-7∑j=1ejRe(f(g(e_(i)x))-f(e_(i)g(x)))j=1 so that it preserves the octonionic para-linearity.In this non-associative category,we introduce the Hom and Tensor functors which constitute an adjoint pair.We establish the Yoneda lemma in terms of the new notion of weak functor.To define the exactness in a non-associative category,we introduce the notion of the enveloping category via a universal property.This allows us to establish the exactness of the Hom functor and Tensor functor.
文摘The concept of para-differential operators over locally compact Vilenkin groups is given and their properties are studied. By means of para-linearization theorem, efforts are made to establish the basic theory of Gibbs-Butzer differential operators.
