相关论文: Uniform measures and convolution on topological gr…
We consider harmonic maps on simply connected Riemann surfaces into the group $\mathrm{U}(n)$ of unitary matrices of order $n$. It is known that a harmonic map with an associated algebraic extended solution can be deformed into a new…
A subclass of complex-valued close-to-convex harmonic functions that are univalent and sense-preserving in the open unit disc is investigated. The coefficient estimates, growth results, area theorem, boundary behavior, convolution and…
Let $\mu$ and $\nu$ be two non-degenerate finite signed Borel measures defined on a proper convex cone of $\mathbb{R}^n$. We prove that if all convolution powers of $\mu$ and $\nu$ are appropriately equal (and non-zero) on a proper concave…
We study the multifractal analysis of self-similar measures arising from random homogeneous iterated function systems. Under the assumption of the uniform strong separation condition, we see that this analysis parallels that of the…
A transfunction is a function which maps between sets of finite measures on measurable spaces. Push-forward operators form one important class of examples of transfunctions and are identified with their respective measurable functions. In…
We generalise results by Sacks and Tanaka concerning measure-theoretic uniformity for hyperarithmetical sets and a basis theorem for $\Pi^1_1$-sets of positive measure to computability and semicomputability relative to the Suslin…
The homogeneous transform has many practical applications outside the realm of mathematics, for instance to represent the proportions of several chemical substances. We aim here to present results about the transformation of measures, which…
We explore boundedness properties in the context of metric measure spaces, of some natural operators of convolution type whose study is suggested by certain transformations used in computer vision.
In this paper we further study links between concentration of measure in topological transformation groups, existence of fixed points, and Ramsey-type theorems for metric spaces. We prove that whenever the group $\Iso(\U)$ of isometries of…
In this paper we extend complex uniform convexity estimates for $\mathbb{C}$ to $ \mathbb{R}^n$ and determine best constants. Furthermore we provide the link to log-Sobolev inequalities and hypercontractivity estimates for ultraspherical…
Theorems and explicit examples are used to show how transformations between self-similar sets (general sense) may be continuous almost everywhere with respect to stationary measures on the sets and may be used to carry well known flows and…
Connectedness, path connectedness, and uniform connectedness are well-known concepts. In the traditional presentation of these concepts there is a substantial difference between connectedness and the other two notions, namely connectedness…
We introduce the notion of Bartlett spectral measure for isometrically invariant random measures on proper metric commutative spaces. When the underlying Gelfand pair corresponds to a higher-rank, connected, simple matrix Lie group with…
We consider mesh functions which are discrete convex in the sense that their central second order directional derivatives are positive. Analogous to the case of a uniformly bounded sequence of convex functions, we prove that the uniform…
We describe and experimentally investigate a method to construct forecasting algorithms for stationary and ergodic processes based on universal measures (or so-called universal data compressors). Using some geophysical and economical time…
What is the ergodic behaviour of numerically computed segments of orbits of a diffeomorphism? In this paper, we try to answer this question for a generic conservative $C^1$-diffeomorphism, and segments of orbits of Baire-generic points. The…
We show that two different ideas of uniform spreading of locally finite measures in the d-dimensional Euclidean space are equivalent. The first idea is formulated in terms of finite distance transportations to the Lebesgue measure, while…
Convolution is conventionally defined as a linear operation on functions of one or more variables which commutes with shifts. Group convolution generalizes the concept to linear operations on functions of group elements representing more…
In this paper we study the existence and uniqueness of fixed points of a class of mappings defined on complete, (sequentially compact) cone metric spaces, without continuity conditions and depending on another function.
We study certain integer valued length functions on triangulated categories and establish a correspondence between such functions and cohomological functors taking values in the category of finite length modules over some ring. The…