In this paper, using a generalized Jacobi-Dunkl translation operator, we prove a generalization of Titchmarsh’s theorem for functions in the k-JacobiDunkl-Lipschitz class defined by the finite differences of order k ∈ N∗ and Sobolev spaces associated with the Jacobi-Dunkl operator.

For all hyperbolic polynomials we proved in [11] a Lipschitz estimate of Jacobi matrices built by orthogonalizing polynomials with respect to measures in the orbit of classical Perron-Frobenius-Ruelle operators associated to hyperbolic polynomial dynamics (with real Julia set). Here we prove that for all sufficiently hyperbolic polynomials this estimate becomes exponentially better when the dim...

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,...

An infinite-dimensional version of Calogero-Moser operator of BC-type and the corresponding Jacobi symmetric functions are introduced and studied, including the analogues of Pieri formula and Okounkov’s binomial formula. We use this to describe all the ideals linearly generated by the Jacobi symmetric functions and show that the deformed BC(m, n) Calogero-Moser operators, introduced in our earl...

The present paper is about Bernstein-type estimates for Jacobi polynomials and their applications to various branches in mathematics. This is an old topic but we want to add a new wrinkle by establishing some intriguing connections with dispersive estimates for a certain class of Schrödinger equations whose Hamiltonian is given by the generalized Laguerre operator. More precisely, we show that ...

We consider congruences and filtrations of Jacobi forms. More specifically, we extend Tate’s theory of theta cycles to Jacobi forms, which allows us to prove a criterion for an analog of Atkin’s U-operator applied to a Jacobi form to be nonzero modulo a prime.

From the classical differential equation of Jacobi fields, one naturally defines the Jacobi operator of a Riemannian manifold with respect to any tangent vector. A straightforward computation shows that any real, complex and quaternionic space forms satisfy that any two Jacobi operators commute. In this way, we classify the real hypersurfaces in quaternionic projective spaces all of whose tange...

We exhibit several families of Jacobi–Videv pseudo-Riemannian manifolds which are not Einstein. We also exhibit Jacobi–Videv algebraic curvature tensors where the Ricci operator defines an almost complex structure.

We establish an integral representations of a right inverses of the Askey-Wilson finite difference operator in an L2 space weighted by the weight function of the continuous q-Jacobi polynomials. We characterize the eigenvalues of this integral operator and prove a q-analog of the expansion of eixy in Jacobi polynomials of argument x. We also outline a general procedure of finding integral repre...

We present a technique for reconstructing a semi-infinite Jacobi operator in the limit circle case from the spectra of two different self-adjoint extensions. Moreover, we give necessary and sufficient conditions for two real sequences to be the spectra of two different self-adjoint extensions of a Jacobi operator in the limit circle case. Mathematics Subject Classification(2000): 47B36, 49N45, ...