Application and Its extension of Maximum Modules Principle in Infinite Domains
This paper leverages the Maximum Modulus Principle to examine a specific class of continuous and analytic functions within a positively oriented n-polygon centered symmetrically at the origin on the complex plane,denoted as f.By assuming that the upper bound of|f|within the n-sided polygon is M,and the upper bound of|f|on a given edge of the n-sided polygon is m,we can derive the upper bound of|f|within a closed triangle,constructed using the origin as the vertex and this edge as the base.In addition,we also extend to a class of analytic functions in the infinite strip region and infinite sector region within the complex plane.Apart from the above,we also extend to two kinds of crescent-shaped regions and the infinite region formed by two parabolas,and some important conclusions are reached.
maximum modulus principleholomorphic functionsquare regionSchwarz symmetry principlesingularity of nature
NETL
NSTL
万方数据
