Related papers: Harmonic balls and two-phase Schwarz function
In this paper, the theory of functions of one complex variable is explored to study linearly full unramified holomorphic two-spheres with constant curvature in $G(2,n)$ satisfying that the generated harmonic sequence degenerates at position…
Spherical wave functions play an important role in the theoretical study of antenna. When they are used to investigate the stored energy outside the circumscribing sphere of the antenna, two different types of modal quality factors appear…
In this paper, we prove a general Schwarz lemma at the boundary for holomorphic mappings from the polydisc to the unit ball in any dimensions. For the special case of one complex variable, the obtained results give the classic boundary…
A decomposition of the Wiener measure based on its quasi-invariance under the group of diffeo- morphisms is proposed. As a result, functional integrals in the Schwarzian theory can be written as the Fourier transform of the integrals in a…
We establish a general result on the existence of partially defined semiconjugacies between rational functions acting on the Riemann sphere. The semiconjugacies are defined on the complements to at most one-dimensional sets. They are…
We point out the conceptual problems related to the application of the standard notion of mass to quarks and recall the arguments that there should be a close connection between the properties of elementary particles and the arena used for…
In this paper, the Schwarz type and Schwarz-Pick type inequalities for solutions of $\alpha$-harmonic equation for $\alpha>-1$ are investigated. By making use of the integral of trigonometric functions, we obtain the two types of…
In the present paper, we introduced the extended bicomplex plane $\bar{\mathbb{T}}$, its geometric model: the bicomplex Riemann sphere, and the bicomplex chordal metric that enables us to talk about the convergence of the sequences of…
We consider the nonlinear Schr{\"o}dinger equation with a harmonic potential in the presence of two combined energy-subcritical power nonlinearities. We assume that the larger power is defocusing, and the smaller power is focusing. Such a…
We define an analogue of the Baernstein star function for a meromorphic function f in several complex variables. This function is subharmonic on the upper half-plane and encodes some of the main functionals attached to f.We then…
Our concern in this paper is to study the qualitative properties for harmonic functions related to the fractional Laplacian. Firstly we classify the polynomials in the whole space and in the half space for the fractional Laplacian defined…
We extend the notions of quantum harmonic analysis, as introduced in R. Werner's paper from 1984 (J. Math. Phys. 25(5)), to abelian phase spaces, by which we mean a locally compact abelian group endowed with a Heisenberg multiplier. In this…
Spherical $t$-design is a finite subset on sphere such that, for any polynomial of degree at most $t$, the average value of the integral on sphere can be replaced by the average value at the finite subset. It is well-known that an…
A collection of algorithms in object-oriented MATLAB is described for numerically computing with smooth functions defined on the unit ball in the Chebfun software. Functions are numerically and adaptively resolved to essentially machine…
We apply the theory of harmonic analysis on the fundamental domain of $SL(2,\mathbb{Z})$ to partition functions of two-dimensional conformal field theories. We decompose the partition function of $c$ free bosons on a Narain lattice into…
We consider the Neumann version of the spherical mean value operator and its variants in the space of smooth functions, distributions and compactly supported ones. Surjectivity and range characterization issues are addressed from the…
We show that every continuous and dually translation invariant valuation on the space of Lipschitz functions on the unit sphere of $\mathbb{R}^n$, $n\ge2$, can be decomposed uniquely into a sum of homogeneous valuations of degree $0$, $1$…
We consider integrals of spherical harmonics with Fourier exponents on the sphere $S^n ,\, n \geq 1$. Such transforms arise in the framework of the theory of weighted Radon transforms and vector diffraction in electromagnetic fields theory.…
In this work we extend the theory of the classical Hardy space $H^1$ to the rational Dunkl setting. Specifically, let $\Delta$ be the Dunkl Laplacian on a Euclidean space $\mathbb{R}^N$. On the half-space $\mathbb{R}_+\times\mathbb{R}^N$,…
In this paper we generalize the classical theorems of Brown and Halmos about algebraic properties of Toeplitz operators to Bergman spaces over the unit ball in several complex variables. A key result, which is of independent interest, is…