We study the class of functions called monodiffric of the second kind by Isaac.They are discrete analogues of holomorphic functions of one or two complex variables.Discrete analogues of the Cauchy-Riemann operator,of ...We study the class of functions called monodiffric of the second kind by Isaac.They are discrete analogues of holomorphic functions of one or two complex variables.Discrete analogues of the Cauchy-Riemann operator,of domains of holomorphy in one discrete variable,and of the Hartogs phenomenon in two discrete variables are investigated.Two fundamental solutions to the discrete Cauchy-Riemann equation are studied:one with support in a quadrant,the other with decay at infinity.The first is easy to construct by induction;the second is accessed via its Fourier transform.展开更多
We study discrete analogues of holomorphic functions of one and two variables, especially those that were called monodiffric functions of the first kind by Rufus Isaacs. Discrete analogues of the Cauchy-Riemann operat...We study discrete analogues of holomorphic functions of one and two variables, especially those that were called monodiffric functions of the first kind by Rufus Isaacs. Discrete analogues of the Cauchy-Riemann operators, domains of holomorphy in one discrete variable, and the Hartogs phenomenon in two discrete variables are investigated.展开更多
文摘We study the class of functions called monodiffric of the second kind by Isaac.They are discrete analogues of holomorphic functions of one or two complex variables.Discrete analogues of the Cauchy-Riemann operator,of domains of holomorphy in one discrete variable,and of the Hartogs phenomenon in two discrete variables are investigated.Two fundamental solutions to the discrete Cauchy-Riemann equation are studied:one with support in a quadrant,the other with decay at infinity.The first is easy to construct by induction;the second is accessed via its Fourier transform.
文摘We study discrete analogues of holomorphic functions of one and two variables, especially those that were called monodiffric functions of the first kind by Rufus Isaacs. Discrete analogues of the Cauchy-Riemann operators, domains of holomorphy in one discrete variable, and the Hartogs phenomenon in two discrete variables are investigated.