Related papers: Embedding theorems for harmonic multifunctional sp…

We develop a Helmholtz-like theorem for differential forms in Euclidean space $E_{n}$ using a uniqueness theorem similar to the one for vector fields. We then apply it to Riemannian manifolds, $R_{n}$, which, by virtue of the…

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.

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…

We obtain a new general sufficient condition for the continuity of the Bergman projection in tube domains over symmetric cones using multifunctional embeddings.We also obtain some sharp embedding relations between the generalized…

In this paper, we present a method of embedding physics data manifolds with metric structure into lower dimensional spaces with simpler metrics, such as Euclidean and Hyperbolic spaces. We then demonstrate that it can be a powerful step in…

This paper focuses on representations of contractively embedded invariant subspaces in several variables. We present a version of the de Branges theorem for $n$-tuples of multiplication operators by the coordinate functions on analytic…

In this paper, we have proved results similar to Tychonoff's Theorem on embedding a space of functions with the topology of pointwise convergence into the Tychonoff product of topological spaces, but applied to the function space $C(X,Y)$…

We consider integration of functions with values in a partially ordered vector space, and two notions of extension of the space of integrable functions. Applying both extensions to the space of real valued simple functions on a measure…

We construct new explicit proper r-harmonic functions on the standard n-dimensional sphere S^n and hyperbolic space H^n for any r\ge 1 and n\ge 2.

We show some of the mathematics that is being developed for the computation of deep inelastic structure functions to three loops. These include harmonic sums, harmonic polylogarithms and a class of difference equations that can be solved…

In this paper, we establish some fixed point theorems in ordered partial metric spaces. An example is given to illustrate our obtained results.

We study integral geometric properties of non-compact harmonic spaces.

A comprehensive approach to Sobolev-type embeddings, involving arbitrary rearrangement- invariant norms on the entire Euclidean space R^n, is offered. In particular, the optimal target space in any such embedding is exhibited. Crucial in…

In this paper, we mainly investigate distortion and covering theorems on some classes of pluriharmonic mappings.

The classical theory of symmetric functions has a central position in algebraic combinatorics, bridging aspects of representation theory, combinatorics, and enumerative geometry. More recently, this theory has been fruitfully extended to…

Embedding words in high-dimensional vector spaces has proven valuable in many natural language applications. In this work, we investigate whether similarly-trained embeddings of integers can capture concepts that are useful for mathematical…

It is well known that the real and imaginary parts of any holomorphic function are harmonic functions of two variables. In this paper we generalize this property to finite-dimensional commutative algebras. We prove that if some basis of a…

We discuss the possibility of extending different versions of the Campbell-Magaard theorem, which have already been established in the context of semi-Riemannian geometry, to the context of Weyl's geometry. We show that some of the known…

We remark that a dyadic version of the Carleson embedding theorem for the Bergman space extends to vector-valued functions and operator-valued measures. This is in contrast to a result by Nazarov, Treil, Volberg in the context of the Hardy…

In this paper we establish a new equivalence relation on the spaces of almost periodic functions which allows us to prove a result like Bohr's equivalence theorem extended to the case of all these functions.