A series expansion for generalized harmonic functions
Markus Klintborg, Anders Olofsson
Abstract
Abstract We consider a class of generalized harmonic functions in the open unit disc in the complex plane. Our main results concern a canonical series expansion for such functions. Of particular interest is a certain individual generalized harmonic function which suitably normalized plays the role of an associated Poisson kernel.
Topics & Concepts
MathematicsSeries (stratigraphy)Harmonic functionPoisson kernelHarmonicSeries expansionMathematical analysisPoisson distributionPure mathematicsClass (philosophy)Kernel (algebra)PhysicsComputer scienceBiologyQuantum mechanicsStatisticsPaleontologyArtificial intelligenceNumerical methods in inverse problemsDifferential Equations and Boundary ProblemsMathematical Analysis and Transform Methods