Related papers: Convolution of $\chi$-orbital Measures on Complex …

When $G_{\mathbb{R}}$ is a real, linear algebraic group, the orbit method predicts that nearly all of the unitary dual of $G_{\mathbb{R}}$ consists of representations naturally associated to orbital parameters $(\mathcal{O},\Gamma)$. If…

In this paper we prove self-improvement properties of strong Muckenhoupt and Reverse H\"older weights with respect to a general Radon measure on $\mathbb{R}^n$. We derive our result via a Bellman function argument. An important feature of…

Let $\mathcal L_1$ be the set of all mappings $f\colon\Z_p\Z_p$ of the space of all $p$-adic integers $\Z_p$ into itself that satisfy Lipschitz condition with a constant 1. We prove that the mapping $f\in\mathcal L_1$ is ergodic with…

We study the properties of reflectionless measures for a Calder\'{o}n-Zygmund operator T. Roughly speaking, these are measures $\mu$ for which T(\mu) vanishes (in a weak sense) on the support of the measure. We describe the relationship…

The Koornwinder-Macdonald multivariable generalization of the Askey-Wilson polynomials is studied for parameters satisfying a truncation condition such that the orthogonality measure becomes discrete with support on a finite grid. For this…

In this paper, a class of holomorphic invariant metrics is introduced on the irreducible classical domains of type I-IV, which are strongly pseudoconvex complex Finsler metrics in the strict sense of M. Abate and G. Patrizio[2]. These…

The volume of the hive polytope (or polytope of honeycombs) associated with a Littlewood- Richardson coefficient of SU(n), or with a given admissible triple of highest weights, is expressed, in the generic case, in terms of the Fourier…

In this paper, we obtain a necessary and sufficient condition for a $U(n)$-invariant complex Finsler metric $F$ on domains in $\mathbb{C}^n$ to be strongly convex, which also makes it possible to investigate relationship between real and…

We investigate classes of shear-free cosmological dust models with irrotational fluid flows within the framework of $f(T)$ gravity. In particular, we use the $1 + 3$ covariant formalism and present the covariant linearised evolution and…

Solving field equations exactly in $f(R,T)$ gravity is one of the difficult task. To do so, many authors have adopted different methods such as assuming both the metric functions, an equation of state (EoS) and a metric function etc.…

We prove that if $(X,\mathsf{d},\mathfrak{m})$ is a metric measure space with $\mathfrak{m}(X)=1$ having (in a synthetic sense) Ricci curvature bounded from below by $K>0$ and dimension bounded above by $N\in [1,\infty)$, then the classic…

Let $H$ be an infinite-dimensional complex Hilbert space. Denote by ${\mathcal G}_{\infty}(H)$ the Grassmannian formed by closed subspaces of $H$ whose dimension and codimension both are infinite. We say that $X,Y\in {\mathcal…

By varying a parameter of a one-dimensional piecewise smooth map, stable periodic orbits are observed. In this paper, complete analytic characterization of these stable periodic orbits is obtained. An interesting relationship between the…

The present paper is the first in a series devoted to the study of asymptotic geometry of Riemann surfaces and their moduli spaces. We introduce the moduli space of hybrid curves as a new compactification of the moduli space of curves,…

Let $X,Y$ be algebraic varieties defined over $\Bbb R$. Assume $Y$ is smooth and $X$ is Gorenstein. Suppose $\varphi:X\to Y$ is a flat $\Bbb R$-morphism such that all the fibers have rational singularities. We show that the pushforward of…

We study eigenvalue problems for the de Rham complex on varying three dimensional domains. Our analysis includes the Helmholtz equation as well as the Maxwell system with mixed boundary conditions and non-constant coefficients. We provide…

Let $X$ be a smooth projective variety over an algebraically closed field, and $f\colon X\to X$ a surjective self-morphism of $X$. The $i$-th cohomological dynamical degree $\chi_i(f)$ is defined as the spectral radius of the pullback…

We extend the results of T. Giordano, I. F. Putnam, C. F. Skau contained in ``$\mathbb Z^d$-odometers and cohomology", Groups Geom. Dyn. 13 (2019), no. 3, P. 909-938, on characterization of conjugacy, isomorphism, and continuous orbit…

We present several operator extensions of the Chebyshev inequality for Hilbert space operators. The main version deals with the synchronous Hadamard property for Hilbert space operators. Among other inequalities, it is shown that if…

We consider a randomly forced Ginzburg-Landau equation on an unbounded domain. The forcing is smooth and homogeneous in space and white noise in time. We prove existence and smoothness of solutions, existence of an invariant measure for the…