Abstract
In this paper we investigate the vector bundle-valued Cauchy and Poisson kernel functions. We compute explicitly matrix-valued eigenfunctions of an invariant differential operator on the classical domain of Type I. Furthermore, a special choice of a vector bundle gives us a matrix-valued Cauchy and Poisson kernel function which satisfies the matrix-valued Laplacian operator on the classical domain of Type I.
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Okamoto, K., Tsukamoto, M. & Yokota, K. Vector Bundle-Valued Poisson and Cauchy Kernel Functions on Classical Domains. Acta Applicandae Mathematicae 63, 323–332 (2000). https://doi.org/10.1023/A:1010741717802
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DOI: https://doi.org/10.1023/A:1010741717802