Related papers: On equisingular approximation of plurisubharmonic …
We prove several results showing that plurisubharmonic functions with various bounds on their Monge-Ampere masses on a bounded hyperconvex domain always admit global plurisubharmonic subextension with logarithmic growth at infinity.
In this paper we develop the p-thinness and the p-fine topology for the asymptotic behavior of p-superharmonic functions at singular points. We consider these as extensions of earlier works on superharmonic functions in dimension 2, on the…
A theorem is proved concerning approximation of analytic functions by multivariate polynomials in the $s$-dimensional hypercube. The geometric convergence rate is determined not by the usual notion of degree of a multivariate polynomial,…
In this paper we consider the approximation of a function by its interpolating multilinear spline and the approximation of its derivatives by the derivatives of the corresponding spline. We derive formulas for the uniform approximation…
A notion of local indicator for a plurisubharmonic function is introduced. The indicator is a certain plurisubharmonic function in the unit polydisc, which controls the behavior of the considered function near a fixed point of its…
In the previous version of this paper we prove a theorem on the boundary behavior of the conical plurisubharmonic measure. However, the proof turns out to be incomplete. In the present version we give a corrected proof of this theorem. We…
Let $G$ be a nonempty bounded domain in a finite-dimensional Euclidean space. The main results are general estimates from below at points from $G$ for an arbitrary subharmonic function $u\not\equiv -\infty$ on the closure of the domain $G$…
We establish the plurisubharmonicity of the envelope of the Poisson functional on almost complex manifolds. That is, we generalize the corresponding result for complex manifolds and almost complex manifolds of complex dimension two.
In this article, we study algebraic decompositions and secondary constructions of almost perfect nonlinear (APN) functions. In many cases, we establish precise criteria which characterize when certain modifications of a given APN function…
All components of complements of discriminant varieties of simple real function singularities are explicitly listed. New invariants of such components (for not necessarily simple singularities) are introduced. A combinatorial algorithm…
On any metric space, I provide an intrinsic characterization of those complex-valued functions which are uniform limits of Lipschitz functions. There are applications to function theory on complete Riemannian manifolds and, in particular,…
We show that on most of the hyperbolic simply connected domains the weighted bounded rational approximation in a natural sup norm is possible only for a very sparse set of holomorphic functions (in contrast to integral approximation). The…
In this paper, we introduce formal sine functions whose coefficients are elements of a generalized harmonic algebra and investigate their properties corresponding to the classical addition formula and Pythagorean theorem. By taking their…
Numerical solutions of differential equations are usually not smooth functions. However, they should resemble the smoothness of the corresponding real solutions in one way or another. In two of our recent papers, a kind of spacial…
We improve our previous generalizations to Arsove's and Ko\lodziej's and Thorbi\"ornson's results concerning the subharmonicity of a function subharmonic with respect to the first variable and harmonic with respect to the second.
We will prove that a function u(x,y) defined on a domain of RpxRq that is subharmonic in one variable and harmonic in the other is (jointly) subharmonic. This solves a long-standing open problem.
We give cohomological criteria for logarithmic good reduction of elliptic surfaces up to modification. Along the way, we prove several more general results about such surfaces in positive characteristic, as well as about log smooth…
Given a compact K\"ahler manifold $X$, a quasiplurisubharmonic function is called a Green function with pole at $p\in X$ if its Monge-Amp\`ere measure is supported at $p$. We study in this paper the existence and properties of such…
We enhance the approximation capabilities of algebraic polynomials by composing them with homeomorphisms. This composition yields families of functions that remain dense in the space of continuous functions, while enabling more accurate…
We study the question of the existence of a dual extremal function for a bounded matrix function on the unit circle in connection with the problem of approximation by analytic matrix functions. We characterize the class of matrix functions,…