论文标题
四分之一平面中非对称拉普拉斯操作员的离散谐波功能
Discrete harmonic functions for non-symmetric Laplace operators in the quarter plane
论文作者
论文摘要
我们在四分之一平面上构建谐波功能，用于离散的拉普拉斯操作员。特别是，这些功能的条件是在边界上消失，而拉普拉斯人则承认与非对称随机步行的过渡概率相关的系数。通过解决为谐波函数生成函数的边界价值问题，我们根据保形映射来推导生成函数的明确表达式。这些映射来自与准对称转移的共形焊接问题，并包含有关谐波功能生长的信息。此外，我们将一组谐波函数描述为对正式功率系列空间的矢量空间同构。
We construct harmonic functions in the quarter plane for discrete Laplace operators. In particular, the functions are conditioned to vanish on the boundary and the Laplacians admit coefficients associated with transition probabilities of non-symmetric random walks. By solving a boundary value problem for generating functions of harmonic functions, we deduce explicit expressions for the generating functions in terms of conformal mappings. These mappings are yielded from a conformal welding problem with quasisymmetric shift and contain information about the growth of harmonic functions. Further, we describe the set of harmonic functions as a vector space isomorphic to the space of formal power series.
