It is known that there is a 1-1 correspondence between the first cohomology of the sheaf O(-k-2) over the projective space and the solutions to the k-Cauchy-Fueter equations on the quaternionic space Hn.We find an exp...It is known that there is a 1-1 correspondence between the first cohomology of the sheaf O(-k-2) over the projective space and the solutions to the k-Cauchy-Fueter equations on the quaternionic space Hn.We find an explicit Radon-Penrose type integral formula to realize this correspondence:given a -closed(0,1)form f with coefficients in the(-k-2)th power of the hyperplane section bundle H-k-2,there is an integral representation Pf such that ι*(Pf) is a solution to the k-Cauchy-Fueter equations,where ι is an embedding of the quaternionic space Hn into C4n.展开更多
Abstract In this article,we investigate the arithmetic behavior of the function D_3(n)which counts the number of 3-regular tripartitions of n.For example,we show that forα≥1 and n≥0,■and
There is little work concerning the properties of quaternionic operators acting on slice regular function spaces defined on quaternions.In this paper,we present an equivalent characterization for the boundedness of th...There is little work concerning the properties of quaternionic operators acting on slice regular function spaces defined on quaternions.In this paper,we present an equivalent characterization for the boundedness of the product operator C_(φ)D^(m) acting on Bloch-type spaces of slice regular functions.After that,an equivalent estimation for its essential norm is established,which can imply several existing results on holomorphic spaces.展开更多
This paper is a continuation of the author＇s paper in 2009, where the abstract theory of fold com- pleteness in Banach spaces has been presented. Using obtained there abstract results, we consider now very general bo...This paper is a continuation of the author＇s paper in 2009, where the abstract theory of fold com- pleteness in Banach spaces has been presented. Using obtained there abstract results, we consider now very general boundary value problems for ODEs and PDEs which poIynomially depend on the spectral parameter in both the equation and the boundary conditions. Moreover, equations and boundary conditions may con- rain abstract operators as well. So, we deal, generally, with integro-differential equations, functional-differential equations, nonlocal boundary conditions, multipoint boundary conditions, integro-differential boundary condi- tions. We prove n-fold completeness of a system of root functions of considered problems in the corresponding direct sum of Sobolev spaces in the Banach Lq-framework, in contrast to previously known results in the Hilbert L2-framework. Some concrete mechanical problems are also presented.展开更多
基金supported by National Natural Science Foundation of China (Grant No.11171298)
文摘It is known that there is a 1-1 correspondence between the first cohomology of the sheaf O(-k-2) over the projective space and the solutions to the k-Cauchy-Fueter equations on the quaternionic space Hn.We find an explicit Radon-Penrose type integral formula to realize this correspondence:given a -closed(0,1)form f with coefficients in the(-k-2)th power of the hyperplane section bundle H-k-2,there is an integral representation Pf such that ι*(Pf) is a solution to the k-Cauchy-Fueter equations,where ι is an embedding of the quaternionic space Hn into C4n.
文摘Abstract In this article,we investigate the arithmetic behavior of the function D_3(n)which counts the number of 3-regular tripartitions of n.For example,we show that forα≥1 and n≥0,■and
基金supported by the National Natural Science Foundation of China(11701422).
文摘There is little work concerning the properties of quaternionic operators acting on slice regular function spaces defined on quaternions.In this paper,we present an equivalent characterization for the boundedness of the product operator C_(φ)D^(m) acting on Bloch-type spaces of slice regular functions.After that,an equivalent estimation for its essential norm is established,which can imply several existing results on holomorphic spaces.
文摘This paper is a continuation of the author＇s paper in 2009, where the abstract theory of fold com- pleteness in Banach spaces has been presented. Using obtained there abstract results, we consider now very general boundary value problems for ODEs and PDEs which poIynomially depend on the spectral parameter in both the equation and the boundary conditions. Moreover, equations and boundary conditions may con- rain abstract operators as well. So, we deal, generally, with integro-differential equations, functional-differential equations, nonlocal boundary conditions, multipoint boundary conditions, integro-differential boundary condi- tions. We prove n-fold completeness of a system of root functions of considered problems in the corresponding direct sum of Sobolev spaces in the Banach Lq-framework, in contrast to previously known results in the Hilbert L2-framework. Some concrete mechanical problems are also presented.
