Related papers: A Note on Gradually Varied Functions and Harmonic …
This paper aims to initialize a dynamical aspect of symbolic integration by studying stability problems in differential fields. We present some basic properties of stable elementary functions and D-finite power series that enable us to…
We prove that every bounded finely plurisubharmonic function can be locally (in the pluri-fine topology) written as the difference of two usual plurisubharmonic functions. As a consequence finely plurisubharmonic functions are continuous…
It is a well-known and elementary fact that a holomorphic function on a compact complex manifold without boundary is necessarily constant. The purpose of the present article is to investigate whether, or to what extent, a similar property…
Functionals (i.e. functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the…
We study the connection between the dimension of certain spaces of harmonic functions on a group and its geometric and algebraic properties. Our main result shows that (for sufficiently "nice" random walk measures) a connected, compactly…
Series representations consisting of spherical harmonics are obtained for characteristic exponents and probability density functions of multivariate stable distributions under various conditions. A esult potentially applicable in a…
We investigate random compact sets with random functions defined thereon, such as polynomials, rational functions, the pluricomplex Green function and the Siciak extremal function. One surprising consequence of our study is that randomness…
Families of hypersurfaces that are level-set families of harmonic functions free of critical points are characterized by a local differential-geometric condition. Harmonic functions with a specified level-set family are constructed from…
The notion of weak cyclic monotonicity of set-valued maps generalizing the cyclic monotonicity is introduced. The existence of solutions of differential inclusions with compact, upper semi-continuous, not necessarily convex right-hand sides…
We propose novel smooth approximations to the classical rounding function, suitable for differentiable optimization and machine learning applications. Our constructions are based on two approaches: (1) localized sigmoid window functions…
Continuous interpolation of real-valued data is characterized by piecewise monotone functions on a compact metric space. Topological total variation of piecewise monotone function f:X->R is a homeomorphism-invariant generalization of 1D…
Suppose that $p \in (1,\infty]$, $\nu \in [1/2,\infty)$, $\mathcal{S}_\nu = \left\{ (x_1,x_2) \in \mathbb{R}^2 \setminus \{(0, 0)\}: |\phi| < \frac{\pi}{2\nu}\right\}$, where $\phi$ is the polar angle of $(x_1,x_2)$. Let $R>0$ and…
We discuss two simple variational approaches to quantum wells. The trial harmonic functions analyzed in an earlier paper give reasonable results for all well depths and are particularly suitable for deep wells. On the other hand, the…
Z. Nehari developed a general technique for obtaining inequalities for conformal maps and domain functions from contour integrals and the Dirichlet principle. Given a harmonic function with singularity on a domain $R$, it associates a…
In this talk, I will discuss the use of harmonic functions to study the geometry and topology of complete manifolds. In my previous joint work with Luen-fai Tam, we discovered that the number of infinities of a complete manifold can be…
We prove that two fixed univariate functions, namely, an arbitrary continuous non-affine function and a concrete affine function, are sufficient to approximate continuous functions of one variable under the operations of addition and…
In this paper, we introduce the concept of nearly convex set-valued mappings and investigate fundamental properties of these mappings. Additionally, we establish a geometric approach for generalized differentiation of nearly convex…
The objective of this paper is to characterize harmonic Hardy spaces and a boundary behavior of harmonic functions on a smooth domain in real Euclidean space.
We prove dilation invariant inequalities involving radial functions, poliharmonic operators and weights that are powers of the distance from the origin. Then we discuss the existence of extremals and in some cases we compute the best…
The regularity of the Hardy-Littlewood maximal function, in both discrete and continuous contexts, and for both centered and noncentered variants, has been subjected to intense study for the last two decades. But efforts so far have…