Related papers: Nonsingular $\alpha$-rigid maps: Short proof
This survey of the recent developments in the investigations of a Leavitt path algebra L of an arbitrary graph E over a field K consists of two parts. In the first part describes how very often a single graph property of E implies multiple…
For essentially bounded functions on a (closed) compact Riemannian manifold, the noncommutative residue and the Dixmier trace formulation of the noncommutative integral are shown to equate to a multiple of the Lebesgue integral. The…
For a locally compact group $H$ with a left Haar measure, we study variable Lebesgue algebra $\mathcal{L}^{p(\cdot)}(H)$ with respect to a convolution. We show that if $\mathcal{L}^{p(\cdot)}(H)$ has bounded exponent, then it contains a…
For a ring R, denote by Spec^R_kappa(Gamma) the kappa-spectrum of the Gamma-invariant of strongly uniform right R-modules. Recent realization techniques of Goodearl and Wehrung show that Spec^R_{aleph_1}(Gamma) is full for suitable von…
Discrete analogs of the Lebedev-Skalskaya transforms are introduced and investigated. It involves series and integrals with respect to the kernels ${\rm Re} K_{\alpha+in}(x), {\rm Im} K_{\alpha+in}(x), x >0, n \in \mathbb{N}, |\alpha | <…
The first result in this study is a non-existence theorem for $\alpha-$harmonic mappings. Additionally, a direct connection between the $\alpha-$ harmonic and harmonic maps is made possible via conformal deformation. Second, the instability…
We deduce mixed quasi-norm estimates of Lebesgue types on semi-continuous convolutions between sequences and functions which may be periodic or possess a weaker form of periodicity in certain directions. In these directions, the Lebesgue…
We extend a classical theorem by H. Lewy to planar $\sigma$-harmonic mappings, that is mappings $U$ whose components $u^1$ and $u^2$ solve a divergence structure elliptic equation ${\rm div} (\sigma \nabla u^i)=0$ , for $i=1,2$. A similar…
We prove that the critical point and the point $1$ have dense orbits for Lebesgue-a.e., parameter pairs in the two-parameter skew-tent family and generalised $\beta$-transformations. As an application, we show that for the generalised…
In this paper, we prove the following result. Let $\alpha$ be any real number between $0$ and $2$. Assume that $u$ is a solution of $$ \left\{\begin{array}{ll} (-\Delta)^{\alpha/2} u(x) = 0 , \;\; x \in \mathbb{R}^n ,\\…
We analyze a real one-parameter family of quasiconformal deformations of a hyperbolic rational map known as {\em spinning}. We show that under fairly general hypotheses, the limit of spinning either exists and is unique, or else converges…
We give two results for deducing dynamical properties of piecewise M\"obius interval maps from their related planar extensions. First, eventual expansivity and the existence of an ergodic invariant probability measure equivalent to Lebesgue…
The lower spectral radius of a set of $d \times d$ matrices is defined to be the minimum possible exponential growth rate of long products of matrices drawn from that set. When considered as a function of a finite set of matrices of fixed…
We give examples of rank-one transformations that are (weak) doubly ergodic and rigid (so all their cartesian products are conservative), but with non-ergodic $2$-fold cartesian product. We give conditions for rank-one infinite…
Index transforms with the product of the associated Legendre functions are introduced. Mapping properties are investigated in the Lebesgue spaces. Inversion formulas are proved. The results are applied to solve a boundary value problem in a…
An elementary proof of a quantitative version of the Riemann-Lebesgue lemma for functions supported on the half line is given. Applications to differential models with memory are discussed.
Under some non-invertibility and irreducibility condition, for nilmanifold Anosov maps with one-dimensional stable bundle, we get the equivalence among the existence of invariant unstable bundle, the existence of topological conjugacy to…
The purpose of this paper is to establish that for any compact, connected C^{\infty} Riemannian manifold there exists a robust family of kernels of increasing smoothness that are well suited for interpolation. They generate Lagrange…
In this note we give a precise statement and a detailed proof for reconstruction problem of weak bialgebra maps. As an application we characterize indecomposability of weak algebras in categorical setting.
It is shown that Gelfand transforms of elements $f\in\lmu$ are constant at almost every fiber $\Pi^{-1}(\{x\})$ of the spectrum of $\lmu$ in the following sense: for each $f\in\lmu$ there is an open dense subset $U=U(f)$ of this spectrum…