In this note we have obtained some novel result on mixed trilateral relations involving extended Jacobi polynomials by group theoretic method which inturn yields the corresponding results involving Hermite, Laguerre and Jacobi polynomials.

Homogeneous Banach spaces determined by the Jacobi translation operator are introduced and studied. Based on this translation operator a Jacobi differential operator is analyzed. Approximation procedures in the homogeneous Banach spaces are presented.

An asymptotic expansion for the Jacobi polynomials and for the functions of the second kind is extended to the case of a weight function that is the product of the Jacobi weight function with an arbitrary positive analytic function.

We classify real hypersurfaces in complex projective spaces whose structure Jacobi operator is Lie parallel in the direction of the structure vector field.  2004 Elsevier B.V. All rights reserved.

We study Jacobi structures on the dual bundle A to a vector bundle A such that the Jacobi bracket of linear functions is again linear and the Jacobi bracket of a linear function and the constant function 1 is a basic function. We prove that a Lie algebroid structure on A and a 1-cocycle φ ∈ Γ(A) induce a Jacobi structure on A satisfying the above conditions. Moreover, we show that this correspo...

The morphic Abel-Jacobi map is the analogue of the classical Abel-Jacobi map one obtains by using Lawson and morphic (co)homology in place of the usual singular (co)homology. It thus gives a map from the group of r-cycles on a complex variety that are algebraically equivalent to zero to a certain “Jacobian” built from the Lawson homology groups viewed as inductive limits of mixed Hodge structur...

This document is a brief overview of the Hamilton-Jacobi theory of Chaplygin systems based on [1]. In this paper, after reducing Chaplygin systems, Ohsawa et al. use a technique that they call Chaplygin Hamiltonization to turn the reduced Chaplygin systems into Hamiltonian systems. This method was first introduced in a paper by Chaplygin in 1911 where he reduced some nonholonomic systems by the...

In this paper, we introduce a kind of character sum which simultaneously generalizes the classical Gauss and Jacobi sums, and show that this “Gauss-Jacobi sum” also specializes to the Kloosterman sum in a particular case. Using the connection to the Kloosterman sums, we obtain in some special cases the upper bound (the “Weil bound”) of the absolute values of the Gauss-Jacobi sums. We also discu...