相关论文: A note on noncommutative holomorphic and harmonic …

Harmonic oscillator in Fock space is defined. Isospectral as well as polynomiality-of-eigenfunctions preserving, translation-invariant discretization of the harmonic oscillator is presented. Dilatation-invariant and…

We study boundary properties of plurisubharmonic functions near real submanifolds of almost complex manifolds.

We study the coefficients of a natural basis for the space of weak harmonic Maass forms of weight $5/2$ on the full modular group. The non-holomorphic part of the first element of this infinite basis encodes the values of the partition…

We discuss the noncommutative generalizations of polynomial algebras which after appropriate completions can be used as coordinate algebras in various noncommutative settings, (noncommutative differential geometry, noncommutative algebraic…

In this paper we prove an isoperimetric inequality for holomorphic functions in the unit polydisc $\mathbf U^n$. As a corollary we derive an inclusion relation between weighted Bergman and Hardy spaces of holomorphic functions in the…

Let u be a subharmonic function in D={|z|<1}. There exist an absolute constant C and an analytic function f in D such that \int_D |u(z)-log|f(z)|| dm(z)<C where m denotes the plane Lebesgue measure. We also consider uniform approximation.

For any closed analytic set X in C^2 there exists a proper holomorphic embedding of the unit disk into C^2 such that the image avoids X.

In this article, we study preserving properties of certain nonlinear integral transforms in some classical families of normalized analytic univalent functions defined in the unit disk. Also, we find sharp pre-Schwarzian norm estimates of…

Some identities for noncommutative perspectives of operator monotone functions in Hilbert spaces aregiven. Applications for weighted operator geometric mean and relative operator entropy are also provided.

This is a survey of current and recent works on deformation quantization and index theorems.

This note provides a complete description of a family of sense preserving harmonic functions in the open unit disk that have the same Jacobians, provided that one of the representatives of this family is known.

We present a family of sense-preserving harmonic mappings in the unit disk related to the classical generalized (analytic) Koebe functions. We prove that these are precisely the mappings that maximize simultaneously the real part of every…

A harmonic self-homeomorphism of a disk does not increase the area of any concentric disk.

We study the behavior of various set-functions under holomorphic motions. We show that, under such deformations, logarithmic capacity varies continuously, while analytic capacity may not.

This paper presents theoretical analysis and software implementation for real harmonics analysis on the special orthogonal group. Noncommutative harmonic analysis for complex-valued functions on the special orthogonal group has been studied…

We study directed weighted graphs which are invariant under a nilpotent and cocompact group action. In particular, we consider the conic section K of the set of positive harmonic functions. We characterise the set of extreme points of the…

We study the variational equations for solitons in noncommutative scalar field theories in an even number of spatial dimensions. We prove the existence of spherically symmetric solutions for a sufficiently large noncommutativity parameter…

In this article, a novel method to compute all discrete polyharmonic functions in the quarter plane for models with small steps, zero drift and a finite group is proposed. A similar method is then introduced for continuous polyharmonic…

We introduce and study properties of certain new multifunctional harmonic spaces in the upper halfspace.We prove several sharp embedding theorems for such multifunctional spaces,these results are new even in the case of a single function.

We use functions of a bicomplex variable to unify the existing constructions of harmonic morphisms from a 3-dimensional Euclidean or pseudo-Euclidean space to a Riemannian or Lorentzian surface. This is done by using the notion of…