Related papers: Morrey-Campanato Functional Spaces for Carnot Grou…

A class of spherical functions is studied which can be viewed as the matrix generalization of Bessel functions. We derive a recursive structure for these functions. We show that they are only special cases of more general radial functions…

This paper is devoted to the study of a natural group topology on the fundamental group which remembers local properties of spaces forgotten by covering space theory and weak homotopy type. It is known that viewing the fundamental group as…

We give a general categorical construction that yields several monads of measures and distributions as special cases, alongside several monads of filters. The construction takes place within a categorical setting for generalized functional…

We study topological groups of monotonic autohomeomorphisms on a generalized ordered space $L$. We find a condition that is necessary and sufficient for the set of all monotonic autohomeomorphisms on $L$ along with the function composition…

We define a class of spaces on which one may generalise the notion of compactness following motivating examples from higher-dimensional number theory. We establish analogues of several well-known topological results (such as Tychonoff's…

We construct a map from fundamental groups of complements to some plane configurations to the groups $G_{n}^{k}$ for large $k$. We discuss connection between the groups $G_{n}^{k}$ for different $G_{n}^{k}$ and their geometric realization.

We first extend the multiplicativity property of arithmetic functions to the setting of operators on the Fock space. Secondly, we use phase operators to get representation of some extended arithmetic functions by operators on the Hardy…

The study of Sobolev inequalities can be divided in two cases: p = 1 and 1 < p < +$\infty$. In the case p = 1 we study here a relaxed version of refined Sobolev inequalities. When p > 1, using as base space classical Lorentz spaces…

It is important to classify covering subgroups of the fundamental group of a topological space using their topological properties in the topologized fundamental group. In this paper, we introduce and study some topologies on the fundamental…

Extending a theorem of Shelah we prove that fundamental groups of Peano continua (locally connected and connected metric compact spaces) are finitely presented if they are countable. The proof uses ideas from geometric group theory.

We study Hamiltonian spaces associated with pairs (E,A), where E is a Courant algebroid and A\subset E is a Dirac structure. These spaces are defined in terms of morphisms of Courant algebroids with suitable compatibility conditions.…

We give norm inequalities for some classical operators in amalgams spaces and in some subspace of Morrey space.

This paper introduces Farey Recursive Functions and investigates their basic properties. Farey Recursive Functions are a special type of recursive function from the rationals to a commutative ring. The recursion of these functions is…

We give different perspectives on the notion of shape for condensed anima. We prove that it recovers more classical notions of shape for topological spaces in the cases of all paracompact compactly generated spaces and all locally…

A generalization of classical mechanics is obtained from a complex parametrization of the phase space. The formalism supports complex Hamiltonian functions describing non-conservative classical mechanical systems. A quantization scheme that…

In this paper, we study connections between the structure of a group and the structure of the group (under pointwise product) of its polynomial functions.

We introduce local iterated function systems and present some of their basic properties. A new class of local attractors of local iterated function systems, namely local fractal functions, is constructed. We derive formulas so that these…

We review the canonical analysis of the Palatini action without going to the time gauge as in the standard derivation of Loop Quantum Gravity. This allows to keep track of the Lorentz gauge symmetry and leads to a theory of Covariant Loop…

For the result on 1-quasiconformal maps, see the paper by Cowling and Ottazzi. The result on quasiconformal maps on Carnot groups with reducible first layer will appear in a forthcoming paper by Enrico Le Donne and Xiangdong Xie.

An example of mechanical system whose configuration space is direct product of a curved space and the local group of rotations, is presented. The system is considered as a model of spinning particle moving in the space. The Hamiltonian…