J. E. McMillan's Area theorem
In this paper, we consider a random entire function defined by a random Dirichlet series where are independent and complex valued variables, . We prove that under natural conditions, for some random entire functions of order zero almost surely every horizontal line is a Julia line without an exceptional value. The result improve a theorem of J. R. Yu: Julia lines of random Dirichlet series. Bull. Sci. Math. 128 (2004), 341–353, by relaxing condition on the distribution of for such function...
This paper is concerned with jump conditions for the double layer potential associated with the two-dimensional Helmholtz equation for Hölder continuous boundary data on arbitrary rectifiable Jordan closed curves in ℝ².