Related papers: The Set of Universal Interpolating Functions is No…

We consider a Nevanlinna-Pick interpolation problem on finite sequences of the unit disc D constrained by Hardy and radial-weighted Bergman norms. We find sharp asymptotics on the corresponding interpolation constants. As another…

In this paper, we present a more complete version of the minimax theorem established in [7]. As a consequence, we get, for instance, the following result: Let $X$ be a compact, not singleton subset of a normed space $(E,\|\cdot\|)$ and let…

The main goal of this paper is to provide a brief survey of recent results which connect together results from different areas of research. It is well known that numerical integration of functions with mixed smoothness is closely related to…

We reformulate and generalize the uniqueness and existence proofs of time-dependent density-functional theory. The central idea is to restate the fundamental one-to-one correspondence between densities and potentials as a global fixed point…

A density function for an algebraic invariant is a measurable function on $\mathbb{R}$ which measures the invariant on an $\mathbb{R}$-scale. This function carries a lot more information related to the invariant without seeking extra data.…

We consider the problem of interpolating a function given on scattered points using Hermite-Birkhoff formulas on the sphere and other manifolds. We express each proposed interpolant as a linear combination of basis functions, the…

It is shown that given a metric space $X$ and a $\sigma$-finite positive regular Borel measure $\mu$ on $X$, there exists a bounded continuous real-valued function on $X$ that is one-to-one on the complement of a set of $\mu$ measure zero.

For Banach spaces of analytic functions on the disc for which the polynomials are dense and their pointt evaluations continuous, we prove the following: If they contain a function such that the limit superior of its modulus is infinite…

Answering a question asked by K.C. Ciesielski and T. Glatzer in 2013, we construct a $C^1$-smooth function $f$ on $[0,1]$ and a set $M \subset \operatorname{graph} f$ nowhere dense in $\operatorname{graph} f$ such that there does not exist…

We are considering typed hierarchies of total, continuous functionals using complete, separable metric spaces at the base types. We pay special attention to the so called Urysohn space constructed by P. Urysohn. One of the properties of the…

We prove the existence of entire functions that achieve universal approximations on certain countable sequences of translation operators .

We prove an implicit function theorem for non-commutative functions. We use this to show that if $p(X,Y)$ is a generic non-commuting polynomial in two variables, and $X$ is a generic matrix, then all solutions $Y$ of $p(X,Y)=0$ will commute…

Accurate approximation of a real-valued function depends on two aspects of the available data: the density of inputs within the domain of interest and the variation of the outputs over that domain. There are few methods for assessing…

The theory of distributions provides generalized solutions for problems which do not have a classical solution. However, there are problems which do not have solutions, not even in the space of distributions. As model problem you may think…

It is shown that there exist such a function g from L^1[0,1] and a weight function 0<u(x)<=1 that g is universal for the weighted space L^1_u[0,1] with respect to signs of its Fourier-Walsh coefficients.

We show that there is no real conflict between the two determinations of the strange sea density from the opposite--sign dimuon production and from the difference of the $F_2$ structure functions measured in neutrino and muon deep inelastic…

In this paper we prove the following: let $\omega(t)$ be a continuous function, increasing in $[0,\infty)$ and $\omega(+0)=0$. Then there exists a series of the form$\sum_{k=-\infty}^\infty C_ke^{ikx}$ with $\sum_{k=-\infty}^\infty C^2_k…

We refer here to the surprising construction made by Giuseppe Peano in 1890. He gave an example of a continuous function (called now the Peano curve) from the unit interval to the whole unit square. We show here the existence of a more…

We study the values taken by the Riemann zeta-function $\zeta$ on discrete sets. We show that infinite vertical arithmetic progressions are uniquely determined by the values of $\zeta$ taken on this set. Moreover, we prove a joint discrete…

In this paper we show that the real differential of any injective slice regular function is everywhere invertible. The result is a generalization of a theorem proved by G. Gentili, S. Salamon and C. Stoppato, and it is obtained thanks, in…