Related papers: On the Weyl function for complex Jacobi matrices
From the literature it is known that orthogonal polynomials as the Jacobi polynomials can be expressed by hypergeometric series. In this paper, the authors derive several contiguous relations for terminating multivariate hypergeometric…
The correspondence between a high-order non symmetric difference operator with complex coefficients and the evolution of an operator defined by a Lax pair is established. The solution of the discrete dynamical system is studied, giving…
In this paper, we consider the recovery of third-order differential operators from two spectra, as well as fourth-order or fifth-order differential operators from three spectra, where these differential operators are endowed with…
The Jacobian conjecture over a field of characteristic zero is considered directly in view of the nonlinear partial differential equations it is associated with. Exploring the integrals of such partial differential equations, this work…
We develop an algorithm to compute Fourier expansions of vector valued modular for Weil representations. As an application, we compute explicit linear equivalences of special divisors on modular varieties of orthogonal type. We define three…
We study spectrum inclusion regions for complex Jacobi matrices which are compact perturbations of the discrete laplacian. The condition sufficient for the lack of discrete spectrum for such matrices is given.
We introduce a new method in the attempt to prove the Jacobian conjecture. In the complex dimension 2 case, we apply this method to prove some new results related the Jacobian conjecture.
This is a tutorial introduction to the representation theory of SU(2) with emphasis on the occurrence of Jacobi polynomials in the matrix elements of the irreducible representations. The last section traces the history of the insight that…
In a recent paper a class of infinite Jacobi matrices with discrete character of spectra has been introduced. With each Jacobi matrix from this class an analytic function is associated, called the characteristic function, whose zero set…
In this paper we introduce a family of rational approximations of the reciprocal of a $\phi$-function involved in the explicit solutions of certain linear differential equations, as well as in integration schemes evolving on manifolds. The…
The Jacobi group is the semi-direct product of the symplectic group and the Heisenberg group. The Jacobi group is an important object in the framework of quantum mechanics, geometric quantization and optics. In this paper, we study the Weil…
We first prove some weighted inequalities for compositions of functions on time scales which are in turn applied to establish some new dynamic Opial-type inequalities in several variables. Some generalizations and applications to partial…
We reformulate time evolution of systems in mixed states in terms of the classical observables of correlators using the Weyl correspondence rule. The resulting equation of motion for the Wigner functional of the density matrix is found to…
A new parameterization of the Jacobi inversion problem is used along with the dynamics of the peaks to describe finite time interaction of peakon weak solutions of the Shallow Water equation.
A procedure to obtain differentiation matrices is extended straightforwardly to yield new differentiation matrices useful to obtain derivatives of complex rational functions. Such matrices can be used to obtain numerical solutions of some…
A remarkable discrete counterpart of the Gaussian function of one continuous variable can be defined by using a Jacobi theta function, that is, as the sum of a convergent series. We extend this approach to Gaussian functions of two…
We study the affine ring of the affine Jacobi variety of a hyper-elliptic curve. The matrix construction of the affine hyper-elliptic Jacobi varieties due to Mumford is used to calculate the character of the affine ring. By decomposing the…
In this note we investigate the discrete spectrum of Jacobi matrix corresponding to polynomials defined by recurrence relations with periodic coefficients. As examples we consider a)the case when period $N$ of coefficients of recurrence…
We investigate the representations of the hyperalgebras associated to the map algebras $\mathfrak g\otimes \mathcal A$, where $\mathfrak g$ is any finite-dimensional complex simple Lie algebra and $\mathcal A$ is any associative commutative…
We consider a new class of quaternionic mappings, associated with the spatial partial differential equations. We describe all mappings from this class using four analytic functions of the complex variable.