Related papers: Notes on the Jacobi equation
We define Jacobi forms of indefinite lattice index, and show that they are isomorphic to vector-valued modular forms also in this setting. We also consider several operations of the two types of objects, and obtain an interesting bilinear…
We study Jacobi matrices on trees whose coefficients are generated by multiple orthogonal polynomials. Hilbert space decomposition into an orthogonal sum of cyclic subspaces is obtained. For each subspace, we find generators and the…
In this paper, we provide conceptional explanations for the geodesic and Jacobi field correspondences for homothetic navigation, and then let them guide us to the shortcuts to some well known flag curvature and S-curvature formulas. They…
In this paper, we define and develop a cohomology and deformation theories of Jacobi-Jordan algebras. We construct a cohomology based on two operators, called zigzag cohomology, and detail the low degree cohomology spaces. We describe the…
We give two characterizations of Jacobians of curves with involution having fixed points in the framework of two particular cases of Welter's trisecant conjecture. The geometric form of each of these characterizations is the statement that…
Quantisation on spaces with properties of curvature, multiple connectedness and non orientablility is obtained. The geodesic length spectrum for the Laplacian operator is extended to solve the Schroedinger operator. Homotopy fundamental…
Let A be a principally polarized abelian threefold over a perfect field k, not isomorphic to a product over the algebraic closure of k. There exists a canonical extension k' of k, of degree 1 or 2, such that A becomes isomorphic to a…
The Jacobian conjecture is an old unsolved problem in mathematics, which has been unsuccessfully attacked from many different angles. We add here another point of view pertaining to the so called formal inverse approach, that of…
We extend integrable systems on quad-graphs, such as the Hirota equation and the cross-ratio equation, to the non-commutative context, when the fields take values in an arbitrary associative algebra. We demonstrate that the…
We derive a sequence of measures whose corresponding Jacobi matrices have special properties and a general mapping of an open quantum system onto 1D semi infinite chains with only nearest neighbour interactions. Then we proceed to use the…
We construct examples of number fields which are not isomorphic but for which their idele class groups are isomorphic. We also construct examples of projective algebraic curves which are not isomorphic but for which their Jacobian varieties…
These are expanded lecture notes of a mini-course whose objectives were to introduce the basic concepts, constructions and techniques of noncommutative geometry, as well as their uses as a framework for modelling quantum spacetime. Key…
We compute the asymptotics of eigenvalues of Jacobi matrices with the zero coefficients on the main diagonal and the off-diagonal coefficients which converge to zero.
The deformation equation and its integrability condition (Bianchi identity) of a non-associative deformation in operad algebra are found. Their relation to the theory of gravity is discussed.
We form the Jacobi theta distribution through discrete integration of exponential random variables over an infinite inverse square law surface. It is continuous, supported on the positive reals, has a single positive parameter, is unimodal,…
One may consider the generalization of Jacobi polynomials and the Jacobi function of the second kind to a general function where the index is allowed to be a complex number instead of a non-negative integer. These functions are referred to…
We review some applications of noncommutative geometry to the study of transverse geometry of Riemannian foliations and discuss open problems.
In this short note we explore the validity of Wente-type estimates for Neumann boundary problems involving Jacobians. We show in particular that such estimates do not in general hold under the same hypotheses on the data for Dirichlet…
In this paper we introduce and discuss some classes of orthogonal polynomials in several non-commuting variables. The emphasis is on a non-commutative version of the orthogonal polynomials on the real line. We introduce recurrence equations…
Our primary objective is to study Pitt-type inequalities on Riemannian symmetric spaces $\mathbb{X}$ of noncompact type, as well as within the framework of Jacobi analysis. Inspired by the spectral gap of the Laplacian on $\mathbb{X}$, we…