Related papers: On planar harmonic functions with identical Jacobi…
This paper investigates positive harmonic functions on a domain which contains an infinite cylinder, and whose boundary is contained in the union of parallel hyperplanes. (In the plane its boundary consists of two sets of vertical…
In this paper we give a unified framework for the construction of complex valued harmonic morphisms from the real, complex and quaternionic Grassmannians and their non-compact duals. This gives a positive answer to the corresponding open…
We show that the iterated images of a Jacobian pair stabilize; that is, the k-th iterates of a polynomial map of complex two-space to itself with a nonzero constant Jacobian determinant all have the same image for sufficiently large k. More…
The Pfaffian structure of the boundary monomer correlation functions in the dimer-covering planar graph models is rederived through a combinatorial / topological argument. These functions are then extended into a larger family of…
We consider the family of all analytic and univalent functions in the unit disk of the form $f(z)=z+a_2z^2+a_3z^3+\cdots$. Our objective in this paper is to estimate the difference of the moduli of successive coefficients, that is $\big |…
We make a progress towards describing the commutants of Toeplitz operators with harmonic symbols on the Bergman space over the unit disk. Our work greatly generalizes several partial results in the field.
These notes briefly discuss basic notions concerning locally compact abelian topological groups and Fourier transforms of functions on them.
We prove that planar homeomorphisms can be approximated by diffeomorphisms in the Sobolev space $W^{1,2}$ and in the Royden algebra. As an application, we show that every discrete and open planar mapping with a holomorphic Hopf differential…
This paper is a contribution to the study of the relations between special functions, Lie algebras and rigged Hilbert spaces. The discrete indices and continuous variables of special functions are in correspondence with the representations…
In these notes we give an interdisciplinary result which links the geometric concept of minimal surfaces with generalized harmonic functions.
We study locally univalent functions $f$ analytic in the unit disc $\mathbb{D}$ of the complex plane such that $|{f"(z)/f'(z)}|(1-|z|^2)\leq 1+C(1-|z|)$ holds for all $z\in\mathbb{D}$, for some $0<C<\infty$. If $C\leq 1$, then $f$ is…
We discuss several new bi-Hamiltonian integrable systems on the plane with integrals of motion of third, fourth and sixth order in momenta. The corresponding variables of separation, separated relations, compatible Poisson brackets and…
This article presents a unified approach to simultaneously compute the Jacobians of several singular matrix transformations in the real, complex, quaternion and octonion cases. Formally, these Jacobians are obtained for real normed division…
We show that the Goldman flows preserve the holomorphic structure on the moduli space of homomorphisms of the fundamental group of a Riemann surface into U(1), in other words the Jacobian.
We study the uniqueness properties of classical semiconjugations for analytic self-maps of the disk, by characterizing them as canonical solutions to certain functional equations. As a corollary, we obtain a complete description of all…
We discuss the occurence and properties of exact singular anyonic wave functions describing stationary states of two identical charged particles moving on a plane and under the influence of a perpendicular uniform magnetic field.
There is a commutative algebra of differential-difference operators, with two parameters, associated to any dihedral group with an even number of reflections. The intertwining operator relates this algebra to the algebra of partial…
It is shown that harmonic functions on some subsets, subharmonic and coinciding everywhere outside of these sets, actually coincide everywhere.
A certain notion of canonical equivalence in quantum mechanics is proposed. It is used to relate quantal systems with discrete ones. Discrete systems canonically equivalent to the celebrated harmonic oscillator as well as the quartic and…
This note reviews some of the recent work on biharmonic conformal maps (see \cite{OC}, Chapter 11, for a detailed survey). It will be focused on biharmonic conformal immersions and biharmonic conformal maps between manifolds of the same…