Related papers: Translating auxiliary symmetries between Schottky …
This paper is the continuation of the study on discrete harmonic analysis related to Jacobi expansions initiated in [1]. Considering the operator $\mathcal{J}^{(\alpha,\beta)}=J^{(\alpha,\beta)}-I$, where $J^{(\alpha,\beta)}$ is the…
In this paper, we study the $S$ transforms of Jacobi processes in the frameworks of free and finite free probability theories. We begin by deriving a partial differential equation satisfied by the free $S$ transform of the free Jacobi…
We present a numerical method to calculate resonances of Schottky surfaces based on Selberg theory, transfer operator techniques and Lagrange-Chebyshev approximation. This method is an alternative to the method based on periodic orbit…
Shape analysis and compuational anatomy both make use of sophisticated tools from infinite-dimensional differential manifolds and Riemannian geometry on spaces of functions. While comprehensive references for the mathematical foundations…
Codebooks with small maximum cross-correlation amplitudes are used to distinguish the signals from different users in CDMA communication systems. In this paper, we first study the Jacobi sums over Galois rings of arbitrary characteristics…
The increasingly common applications of machine-learning schemes to atomic-scale simulations have triggered efforts to better understand the mathematical properties of the mapping between the Cartesian coordinates of the atoms and the…
In [Yu.M. Berezansky, E. Lytvynov, D. A. Mierzejewski, Ukrainian Math. J. 55 (2003), 853--858 ], the Jacobi field of a L\'evy process was derived. This field consists of commuting self-adjoint operators acting in an extended (interacting)…
Landen transformation formulas, which connect Jacobi elliptic functions with different modulus parameters, were first obtained over two hundred years ago by changing integration variables in elliptic integrals.We rediscover known results as…
Isothermic surfaces are surfaces which allow a conformal curvature line parametrisation. They form an integrable system, and Darboux transforms of isothermic surfaces obey Bianchi permutability: for two distinct spectral parameters the…
By Koebe's retrosection theorem, every closed Riemann surface of genus $g \geq 2$ is uniformized by a Schottky group. Marden observed that there are Schottky groups that are not classical ones, that is, they cannot be defined by a suitable…
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…
We address various aspects of a widely used tool in quantum information theory: the Choi-Jamiolkowski isomorphism [A. Jamiolkowski, Rep. Math. Phys., 3, 275 (1972)]. We review different versions of the isomorphism, their properties and…
For a family of Jacobians of smooth pointed curves there is a notion of tautological algebra. There is an action of $\mathfrak{sl}_2$ on this algebra. We define and study a lifting of the Polishchuk operator, corresponding to $f\in…
We define the Jacobian of a Riemann surface with analytically parametrized boundary components. These Jacobians belong to a moduli space of ``open abelian varieties'' which satisfies gluing axioms similar to those of Riemann surfaces, and…
We introduce and study (strict) Schottky G-bundles over a compact Riemann surface X, where G is a connected reductive algebraic group. Strict Schottky representations are shown to be related to branes in the moduli space of G-Higgs bundles…
The Jacobi-Stirling numbers and the Legendre-Stirling numbers of the first and second kind were first introduced in [6], [7]. In this paper we note that Jacobi-Stirling numbers and Legendre-Stirling numbers are specializations of elementary…
The Jacobi curve of an extremal of optimal control problem is a curve in a Lagrangian Grassmannian defined up to a symplectic transformation and containing all information about the solutions of the Jacobi equations along this extremal. In…
Physically meaningful periodic solutions to certain integrable partial differential equations are given in terms of multi-dimensional theta functions associated to real Riemann surfaces. Typical analytical problems in the numerical…
In the theory of Teichm\"uller space of Riemann surfaces, we consider the set of Riemann surfaces which are quasiconformally equivalent. For topologically finite Riemann surfaces, it is quite easy to examine if they are quasiconformally…
The research on spectral inequalities for discrete Schrodinger Operators has proved fruitful in the last decade. Indeed, several authors analysed the operator's canonical relation to a tridiagonal Jacobi matrix operator. In this paper, we…