We present a new proof of the Poisson integral formula for harmonic functions using the methods of representation theory. In doing so, we exhibit the irreducible subspaces and unitary structure of a representation of the group SU(1,1) of 2 x 2 complex generalized special unitary matrices. Our arguments illustrate a technique that can be used to prove similar reproducing formulas in higher dimensions and for other classes of functions. Our paper should be accessible to readers with minimal knowledge of complex analysis.
Prof. Matvei Libine, Department of Mathematics, Indiana University
"The Poisson Integral Formula and Representations of SU(1,1),"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 12
, Article 1.
Available at: https://scholar.rose-hulman.edu/rhumj/vol12/iss2/1