Recently Lapointe et. al. [3] have expressed Jack Polynomials as determinants in monomial symmetric functions mλ. We express these polynomials as determinants in elementary symmetric functions eλ, showing a fundamental symmetry between these two expansions. Moreover, both expansions are obtained indifferently by applying the Calogero-Sutherland operator in physics or quasi Laplace Beltrami oper...

Spherical harmonics of degree l are the functions on the unit 2-sphere which satisfy ∆f = l(l + 1)f for the Laplace-Beltrami operator ∆. They form an irreducible representation of SO(3) of dimension 2l + 1 and are the restrictions to the sphere of homogeneous polynomials f(x1, x2, x3) of degree l which solve Laplace’s equation in R. This paper concerns a curious relationship between the case l ...

Erratum : A Geometrical Theory of Jacobi Forms of Higher Degree Jae-Hyun Yang Department of Mathematics, Inha University, Incheon 402-751, Korea e-mail : [email protected] Erratum In the article A Geometrical Theory of Jacobi Forms of Higher Degree by JaeHyun Yang [Kyungpook Math. J., 40(2)(2000), 209-237], the author presents the Laplace-Beltrami operator ∆g,h of the Siegel-Jacobi space (Hg,h,...

Compressed manifold modes are locally supported analogues of eigenfunctions of the Laplace-Beltrami operator of a manifold. In this paper we describe an algorithm for the calculation of modes for discrete manifolds that, in experiments, requires on average 47% fewer iterations and 44% less time than the previous algorithm. We show how to naturally order the modes in an analogous way to eigenfun...

We consider direct and inverse scattering for the Laplace-Beltrami operator with electromagnetic potentials in domains with smooth surfaces upon which we impose interface conditions. The boundary conditions used encompass physical models of imperfect transmission arising in acoustics, quantum scattering, semiconductors, and geophysics. We prove uniqueness of the location of the surfaces and the...

An Ad K invariant inner product on the Lie algebra of a compact connected Lie group K extends to a Hermitian inner product on the Lie algebra of the complexified Lie group Kc. The Laplace-Beltrami operator, ∆, on Kc induced by the Hermitian inner product determines, for each number a > 0, a Green’s function ra by means of the identity (a2−∆/4)−1 = ra∗. The Hilbert space of holomorphic functions...

This paper solves the problem of computing conformal structures of general 2manifolds represented as triangular meshes. We approximate the De Rham cohomology by simplicial cohomology and represent the Laplace-Beltrami operator, the Hodge star operator by linear systems. A basis of holomorphic one-forms is constructed explicitly. We then obtain a period matrix by integrating holomorphic differen...

Let (M, g, σ) be a compact Riemannian surface equipped with a spin structure σ. For any metric ḡ onM , we denote by ΣḡM the spinor bundle associated to ḡ. We let ∆ḡ be the Laplace-Beltrami operator acting on smooth functions of M and Dḡ be the Dirac operator acting on smooth spinor fields with respect to the metric ḡ. We also denote by μ1(ḡ) (resp. λ1(ḡ)) the smallest positive eigenvalue of ∆ḡ ...