We obtain $$L^p$$ estimates for Toeplitz operators on the generalized Hartogs triangles $$\mathbb {H}_\gamma = \{(z_1,z_2) \in \mathbb {C}^2\,{:}\, |z_1|^\gamma \!< |z_2|<1\}$$ two classes of positive radial symbols, one a power distance to origin, and other boundary.

In this paper, we provide a survey of results on analytic and plurisubharmonic extensions functions that have thin set singularities along fixed direction. We show the advantages using pluripotential theory Jacobi–Hartogs series for description singular such functions.

We recall the complex structure on generalized loop spaces Wk,2(S,X), where S is a compact real manifold with boundary and X manifold, prove Hartogs-type extension theorem for holomorphic maps from certain domains in spaces.

We often need to refer to adjacent elements (e.g., vertices, edges and faces) in triangle meshes for rendering, mesh simplification and other processes. It is, however, sometimes impossible to prepare the enormous memory needed to represent element connectivity in gigantic triangle meshes. We proposed a memory efficient scheme for referring to adjacent faces around a vertex in non-manifold tria...

Isosceles trapezoids are dissected into three similar triangles and rearranged to form two additional isosceles trapezoids. Moreover, triangle centers, one from each similar triangle, form the vertices of a centric triangle which has special properties. For example, the centroidal triangles are congruent to each other and have an area one-ninth of the area of the trapezoids; whereas, the circum...

In this paper, we present a finite-granularity, loading algorithm for a Discrete Multitone (DMT) modulation system. The proposed algorithm offers significant implementational advantages over the well-known water-pouring method and the earlier Hughes-Hartogs algorithm, while typically suffering only negligible performance degradation relative to the optimal solution. We also present simulation r...

This article gives an introduction to the multiple Dirichlet series arising from sums of twisted automorphic L-functions. We begin by explaining how such series arise from Rankin-Selberg constructions. Then more recent work, using Hartogs’ continuation principle as extended by Bochner in place of such constructions, is described. Applications to the nonvanishing of Lfunctions and to other probl...