Generalized holomorphic Szeg kernel in 3D spheroids
Monogenic orthogonal polynomials over 3D prolate spheroids were previously introduced and shown to have some remarkable properties. In particular, the underlying functions take values in the quaternions (identified with R4 R 4 ), and are generally assumed to be nullsolutions of the well known MoisilThodoresco system. In this paper, we show that these polynomial functions play an important role in defining the Szeg kernel function over the surface of 3D (prolate) spheroids. As a concrete application, we prove an explicit expression of the monogenic Szeg kernel function over 3D (prolate) spheroids and present two numerical examples.
szeg kernel function quaternion analysis ferrers associated legendre functions chebyshev polynomials hyperbolic functions prolate spheroidal monogenics