Using a quaternionic calculus, the Christoffel, Darboux, Goursat, and spectral transformations for discrete isothermic nets are described, with their interrelations. The Darboux and spectral transformations are used to define discrete analogs for cmc-1 surfaces in hyperbolic space and to obtain a discrete version of Bryant's Weierstrass type representation.

Szegö quadrature formulas represent the analogue on the unit circle of the well-known Gauss–Christoffel quadratures for intervals of the real line. In the present work, Szegö formulas are revised and an application to the computation of the Fourier transform given. 2006 Elsevier Inc. All rights reserved.

Generalized Lagrange-Weyl structures and compatible connections are introduced as a natural generalization of similar notions from Riemannian geometry. Exactly as in Riemannian case, the compatible connection is unique if certain symmetry conditions with respect to vertical and horizontal Christoffel symbols are imposed. 2000 Math. Subject Classification: 53C60.

Motivated both by digital filter design and polynomial-based matrix iteration methods, we study Green’s function for the complement of a union of disjoint closed intervals. The key tool is the Schwarz–Christoffel map. Asymptotic analysis produces simple and useful leading terms for Green’s function and the associated equilibrium distribution. Our results are applied to optimal lowpass filters a...

A Chern-Simons action written with Christoffel Symbols has a natural gauge symmetry of diffeomorphisms. This Chern-Simons action will induce a WessZumio-Witten model on the boundary of the manifold. If we restrict the diffeomorphisms to chiral diffeomorphism, the Wess-Zumio-Witten model is equivalent to a quantum Liouville action. email: [email protected]

We give a uniform and elementary treatment of many classical and new triply periodic minimal surfaces in Euclidean space, based on a Schwarz-Christoffel formula for periodic polygons in the plane. Our surfaces share the property that vertical symmetry planes cut them into simply connected pieces. 2000 Mathematics Subject Classification. Primary 53A10; Secondary 49Q05, 53C42.

We derive an elementary formula for Janossy densities for determinantal point processes with a finite rank projection-type kernel. In particular, for β = 2 polynomial ensembles of random matrices we show that the Janossy densities on an interval I ⊂ R can be expressed in terms of the Christoffel-Darboux kernel for the orthogonal polynomials on the complement of I.

We derive an elementary formula for Janossy densities for determinantal point processes with a finite rank projection-type kernel. In particular, for β = 2 polynomial ensembles of random matrices we show that the Janossy densities on an interval I ⊂ R can be expressed in terms of the Christoffel-Darboux kernel for the orthogonal polynomials on the complement of I.

We show that the computational complexity of Riemann mappings can be bounded by the complexity needed to compute conformal mappings locally at boundary points. As a consequence we get first formally proven upper bounds for Schwarz-Christoffel mappings and, more generally, Riemann mappings of domains with piecewise analytic boundaries.