Related papers: Note on the convolution of harmonic mappings
We study locally harmonic maps between a Riemann surface or Lorentz surface $M$ and a Riemann surface or Lorentz surface $N$. {All four cases are studied in a unified way}. All four cases are written using a unified formalism. Therefore…
In this note, we generalize biharmonic equation for rotationally symmetric maps ([4], [16], [10]) to equivariant maps between model spaces and use it to give a complete classification of rotationally symmetric conformal biharmonic maps from…
We study the Dirichlet problem for harmonic maps between hyperbolic planes, under the assumption that the Euclidean harmonic extension of the boundary map is quasiconformal.
We study the convolution function $$ C[f(x)] := \int_1^x f(y)f({x\over y}) {{\rm d} y\over y} $$ when $f(x)$ is a suitable number-theoretic error term. Asymptotics and upper bounds for $C[f(x)]$ are derived from mean square bounds for…
This work introduces a Hamiltonian approach to regularization and linearization of central-force particle dynamics through a new canonical extension of the so-called "projective decomposition". The regularization scheme is formulated within…
We introduce and study a mathematical framework for a broad class of regularization functionals for ill-posed inverse problems: Regularization Graphs. Regularization graphs allow to construct functionals using as building blocks linear…
The historical developments of conformal transformations and symmetries are sketched: Their origin from stereographic projections of the globe, their blossoming in two dimensions within the field of analytic complex functions, the generic…
In the present paper we revisit the Helmholtz equation on the Euclidean plane and make some remarks on normalization constants and completeness of wave function sets. The coefficients of interbasis expansions are also reconsidered.
In this paper, we establish several new inequalities for some twice differantiable mappings. Then, we apply these inequalities to obtain new midpoint, trapezoid and perturbed trapezoid rules. Finally, some applications for special means of…
The free metaplectic transformation (FMT) is widely used in many fields such as filter design, pattern recognition, image processing and optics. In order to obtain a more concise and intuitive convolution form, this paper studies two kinds…
In this paper, we characterize the rectifiability (both uniform and not) of an Ahlfors regular set, E, of arbitrary co-dimension by the behavior of a regularized distance function in the complement of that set. In particular, we establish a…
The subject of features normalization plays an important central role in data representation, characterization, visualization, analysis, comparison, classification, and modeling, as it can substantially influence and be influenced by all of…
It is shown that a band limited function on a non-compact symmetric space can be reconstructed in a stable way from some countable sets of values of its convolution with certain distributions of compact support. A reconstruction method in…
In a recent paper the first and the third authors introduced the notion of horizontal \alpha-harmonic map, with respect to a given C^1 planes distribution P_T on all R^m. The goal of this paper is to investigate compactness and quantization…
In earlier work the authors have extended Nehari's well-known Schwarzian derivative criterion for univalence of analytic functions to a univalence criterion for canonical lifts of harmonic mappings to minimal surfaces. The present paper…
There is growing body of learning problems for which it is natural to organize the parameters into matrix, so as to appropriately regularize the parameters under some matrix norm (in order to impose some more sophisticated prior knowledge).…
We describe recent nonlinear analytic approximation tools in the classical setting of Hardy spaces in the upper half plane and show how to transfer them to the higher dimensional real setting of harmonic functions in upper half spaces. It…
This paper is devoted to the classification problems concerning extended deformations of convex polyhedra and real hyperplane arrangements in the following senses: combinatorial equivalence of face posets, normal equivalence on normal fans…
Dimensional regularization is used to derive the equations of motion of two point masses in harmonic coordinates. At the third post-Newtonian (3PN) approximation, it is found that the dimensionally regularized equations of motion contain a…
This paper describes a method of calculating the transforms, currently obtained via Fourier and reverse Fourier transforms. The method allows calculating efficiently the transforms of a signal having an arbitrary dimension of the digital…