In this paper we characterize off-diagonal Carleson embeddings for both Hardy-Orlicz spaces and Bergman-Orlicz of the upper-half plane. We use these results to obtain embedding relations pointwise multipliers between spaces.

In this paper, we apply Shannon wavelet and Galerkin method to deal with the numerical solution of the natural boundary integral equation of plane elasticity probem in the upper half-plane. The fast algorithm is given and only 3K entries need to be computed for one 4K × 4K stiffness matrix. Keyword: plane elasticity problem, natural integral equation, Shannon wavelet, Galerkin-wavelet method.

In this paper, we construct an affine model of a Riemann surface with flat Riemannian metric associated to Schwarz–Christoffel mapping the upper half plane onto rational triangle. We explain relation between geodesics on and billiard motions in regular stellated n-gon complex plane.

Orders in indefinite quaternion algebras provide Fuchsian groups acting on the Poincare half-plane, used to construct the associated Shimura curves. We explain how, by using embedding theory, the elements of those Fuchsian groups depend on representations of integers by suitable ternary quadratic forms. Thus the explicit computation of those representations leads to explicit presentations and f...

In this article, the recent results on basic boundary value problems of complex analysis are surveyed for complex model equations and linear elliptic complex partial differential equations of arbitrary order on simply connected bounded domains, particularly in the unit disc, on unbounded domains such as upper half plane and upper right quarter plane and on multiply connected domains containing ...

We use the biorthogonal multiwavelets related by differentiation constructed in previous work to construct compactly supported biorthogonal multiwavelet bases for the space of vector fields on the upper half plane R+ such that the reconstruction wavelets are divergence-free and have vanishing normal components on the boundary of R+. Such wavelets are suitable to study the Navier–Stokes equation...

We investigate the roots of relative Steiner polynomials of convex bodies. In dimension 3 we give a precise description of their location in the complex plane and we study the analogous problem in higher dimensions. In particular, we show that the roots (in the upper half plane) form a convex cone; for dimensions ≤ 9 this cone is completely contained in the (open) left half plane, which is not ...