相关论文: An egg-yolk principle and exponential integrabilit…

Since the nonlinear integral transforms $J_{\alpha}[f](z) = \int_{0}^{z}(f'(u))^{\alpha} du$ and $I_{\alpha}[f](z) =\int_0^z (f(u)/u)^{\alpha} du$ with a complex number $\alpha$ have been introduced, a great number of studies were dedicated…

We consider the convexity properties of distortion functionals, particularly the linear distortion, defined for homeomorphisms of domains in Euclidean $n$-spaces, $n\geq 3$. The inner and outer distortion functionals are lower…

The article is devoted to holomorphic and meromorphic functions of quaternion and octonion variables. New classes of quasi-conformal and quasi-meromorphic mappings are defined and investigated. Properties of such functions such as their…

One of the celebrated results by Riesz \cite{Rie} is the Riesz conjugate functions theorem for analytic functions in the complex plane $\mathbb{C}$. The study on the Riesz conjugate functions theorem for functions in higher dimensional…

The Fatou-Julia iteration theory of rational and transcendental entire functions has recently been extended to quasiregular maps in more than two real dimensions. Our goal in this paper is similar; we extend the iteration theory of analytic…

Michael's selection theorem implies that a closed convex nonempty-valued mapping from the Sorgenfrey line to a euclidean space is inner semicontinuous if and only if the mapping can be represented as the image closure of right-continuous…

Chirped sinosoids and interferometric phase plots are functions that are not periodic, but are the composition of a smooth function and a periodic function. These functions functions factor into a pair of maps: from their domain to a…

Let $\overline{\mathbb{D}}$ be the closure of the unit disk $\mathbb{D}$ in the complex plane $\mathbb{C}$ and $g$ be a continuous function in $\overline{\mathbb{D}}$. In this paper, we discuss some characterizations of elliptic mappings…

Green's functions are highly useful in analyzing the dynamical behavior of polynomials in their escaping set. The aim of this paper is to construct an analogue of Green's functions for planar quasiregular mappings of degree two and constant…

In this paper, we consider mappings on uniform domains with exponentially integrable distortion whose Jacobian determinants are integrable. We show that such mappings can be extended to the boundary and moreover these extensions are…

The main goal of this article is to bring together the theories of holomorphic iteration in the unit disc and semigroups of holomorphic functions. We develop a technique that allows us to partially embed the orbit of a holomorphic self-map…

In this paper we show that the equivalences between certain properties of closed subanalytic sets proved by E. Bierstone and P. Milman in \cite{[BM-1]} hold for closed sets definable in quasianalytic o-minimal structures. In particular we…

We give a new proof of the result that if f and g are transcendental entire functions, then the composite function f(g) has infinitely many fixed points. The method yields a number of generalization of this result. In particular, it extends…

We construct differential algebras in which spaces of (one-dimensional) periodic ultradistributions are embedded. By proving a Schwartz impossibility type result, we show that our embeddings are optimal in the sense of being consistent with…

We study quasi-Monte Carlo integration for twice differentiable functions defined over a triangle. We provide an explicit construction of infinite sequences of points including one by Basu and Owen (2015) as a special case, which achieves…

We study the connection between cyclic quasi-monotonicity and quasi-convexity, focusing on whether every cyclically quasi-monotone (possibly multivalued) map is included in the normal cone operator of a quasi-convex function, in analogy…

We study energy functionals associated with quasi-linear Schr\"odinger operators on infinite graphs, and develop characterisations of (sub-)criticality via Green's functions, harmonic functions of minimal growth and capacities. We proof a…

Commensurability is of paramount importance in numerous strongly interacting electronic systems. In the Fractional Quantum Hall effect, a rich cascade of increasingly narrow plateaux appear at larger denominator filling fractions. Rich…

We introduce a new intrinsic metric in subdomains of a metric space and give upper and lower bounds for it in terms of well-known metrics. We also prove distortion results for this metric under quasiregular maps.

We establish exponential laws for certain spaces of differentiable functions over a valued field K. For example, we show that the topological vector spaces C^{r,s}(U x V,E) and C^r(U,C^s(V,E)) are isomorphic if U and V are open subsets of…