Orthonormalreihenentwicklungen für gewisse quasikonforme Normalabbildungen

  • Erich Hoy

    Friedberg, Germany


The paper deals with the construction of solutions for the equation with in a finitely connected region and const in the complementary continua of . The construction starts with well-known and in a simple way explicitly computable analytic functions in , and series for the solutions are received only by the use of orthogonalization processes. These series converge in the well-known norm produced by the integral over of the square of derivative’s absolute value. If the boundary of consists of analytic Jordan curves only, then there is even an upper bound of the form with and for the supremum of deviation of the -th partial sum of these series from the sought solutions over . Simple methods are given for the computation of .The results are generalized for the case, that in analytic functions take the place of the constants . At the conclusion a possible extension of the procedure to more generalized functions is discussed.

Cite this article

Erich Hoy, Orthonormalreihenentwicklungen für gewisse quasikonforme Normalabbildungen. Z. Anal. Anwend. 3 (1984), no. 6, pp. 503–521

DOI 10.4171/ZAA/125