On $L^2$-eigenfunctions of Twisted Laplacian on curved surfaces and suggested orthogonal polynomials

Details On $L^2$-eigenfunctions of Twisted Laplacian on curved surfaces and suggested orthogonal polynomials On $L^2$-eigenfunctions of Twisted Laplacian on curved surfaces and suggested orthogonal polynomials

2010-03-29

arxiv.org/abs/1003.5501v1

Oper. Matrices 4 (2010), no. 4, 533--540

Mathematics

Spectral Theory

This will appear in the Proceeding of ICOAA08 that will be published by the Journal of Operators and Matrices.

Scientific paper

We show in a unified manner that the factorization method describes completely the $L^2$-eigenspaces associated to the discrete part of the spectrum of the twisted Laplacian on constant curvature Riemann surfaces. Subclasses of two variable orthogonal polynomials are then derived and arise by successive derivations of elementary complex valued functions depending on the geometry of the surface.

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