On the mulitplier of a repelling fixed point.
Let be a rectifiable Jordan curve in the finite complex plane which is regular in the sense of Ahlfors and David. Denote by the space of all complex-valued functions on which are square integrable w.r. to the arc-length on . Let stand for the space of all real-valued functions in and put Since the Cauchy singular operator is bounded on , the Neumann-Poincaré operator sending each into is bounded on . We show that the inclusion characterizes the circle in the class of all...
We give a bound for the number of coincidence of two morphisms between given compact Riemann surfaces (complete complex algebraic curves). Our results generalize well known facts about the number of fixed points of an automorphism.
Making use of a modified Hadamard product, or convolution, of analytic functions with negative coefficients, combined with an integral operator, we study when a given analytic function is in a given class. Following an idea of U. Bednarz and J. Sokół, we define the order of convolution consistence of three classes of functions and determine a given analytic function for certain classes of analytic functions with negative coefficients.