Related papers: Jacobi structures and Spencer operators

In this paper a Bass-Serre theory in the groupoid setting is developed and a structure theorem is established. Any groupoid action without inversion of edges on a forest induces a graph of groupoids, while any graph of groupoids satisfying…

This review article intends to introduce the reader to non-integrable geometric structures on Riemannian manifolds and invariant metric connections with torsion, and to discuss recent aspects of mathematical physics--in particular…

We define Dirac pairs on Jacobi algebroids, which is a generalization of Dirac pairs on Lie algebroids introduced by Kosmann-Schwarzbach. We show the relationship between Dirac pairs on Lie and on Jacobi algebroids, and that Dirac pairs on…

The paper concerns with infinite symmetric block Jacobi matrices $\bf J$ with $p\times p$-matrix entries. We present new conditions for general block Jacobi matrices to be selfadjoint and have discrete spectrum. In our previous papers there…

We develop various properties of symmetric generalized complex structures (in connection with their holomorphic space and B-field transformations), which are analogous to the well-known results of Gualtieri on skew-symmetric generalized…

This is the appendix of the paper [T. Arias-Marco, Constant Jacobi osculating rank of $U(3)/(U(1) \times U(1) \times U(1))$, Arch. Math. (Brno) 45 (2009), 241--254] where we obtain an interesting relation between the covariant derivatives…

We study the integrability of Poisson and Dirac structures that arise from quotient constructions. From our results we deduce several classical results as well as new applications. We also give explicit constructions of Lie groupoids…

We present a transplantation theorem for Jacobi coefficients in weighted spaces. In fact, by using a discrete vector-valued local Calder\'{o}n-Zygmund theory, which has recently been furnished, we prove the boundedness of transplantation…

We extend to manifolds endowed with a general geometric structure, the classical notions of gradient as well as Laplace operator, and provide some of their natural properties.

We give a simple proof of Borg type uniqueness Theorems for periodic Jacobi operators with matrix valued coefficients.

There is a commutative algebra of differential-difference operators, with two parameters, associated to any dihedral group with an even number of reflections. The intertwining operator relates this algebra to the algebra of partial…

Motivated by the desire of finding a geometric interpretation to the Yamabe equation on groups of Heisenberg type, we define a geometric structure on manifolds modelled locally on these groups, which we call contact structure of Heisenberg…

In this paper, we present a relation between Jacobi-Reeb dynamics and the dynamics associated with a mechanical Hamiltonian system with respect to a linear Poisson structure on a vector bundle. For this purpose, we will use the so-called…

Poisson brackets admit infinitesimal symmetries which are encoded using oriented graphs; this construction is due to Kontsevich (1996). We formulate several open problems about combinatorial and topological properties of the graphs…

Let $J$ be a Jacobi operator on $\ell^2\left(\mathbb{Z}\right)$. We prove an eigenfunction expansion theorem for the singular part of $J$ using subordinate solutions to the eigenvalue equation. We exploit this theorem in order to show that…

The Jacobian is an algebraic invariant of a graph which is often seen in analogy to the class group of a number field. In particular, there have been multiple investigations into the Iwasawa theory of graphs with the Jacobian playing the…

The classical Kepler-Coulomb system in 3 dimensions is well known to be 2nd order superintegrable, with a symmetry algebra that closes polynomially under Poisson brackets. This polynomial closure is typical for 2nd order superintegrable…

By Poissonization of Jacobi structures on real three-dimensional Lie groups $\mathbf{G}$ and using the realizations of their Lie algebras, we obtain integrable bi-Hamiltonian systems on $\mathbf{G}\otimes \mathbb{R}$.

In this second paper of the series we specify general theory developed in the first paper. Here we study the structure of Jacobi fields in the case of an analytic system and piece-wise analytic control. Moreover, we consider only…

We study potential operators (Riesz and Bessel potentials) associated with classical Jacobi and Fourier-Bessel expansions. We prove sharp estimates for the corresponding potential kernels. Then we characterize those $1 \le p,q \le \infty$,…