Related papers: The multipole Lempert function is monotone under i…

The Lempert function for a set of poles in a domain of $\mathbb C^n$ at a point $z$ is obtained by taking a certain infimum over all analytic disks going through the poles and the point $z$, and majorizes the corresponding multi-pole…

We study the problem of the product property for the Lempert function with many poles and consider some properties of this function mostly for plane domains.

Motivated by existing results, we present some completely monotonic functions involving the polygamma functions.

Given a domain $\Omega \subset \mathbb C$, the Lempert function is a functional on the space $Hol (\D,\Omega)$ of analytic disks with values in $\Omega$, depending on a set of poles in $\Omega$. We generalize its definition to the case…

We review a few results concerning interpolation of monotone functions on infinite lattices, emphasizing the role of set-theoretic considerations. We also discuss a few open problems.

In this paper has been proved the pluripolarity of graphs of algebroid functions

We prove that the Lempert function of the symmetrized polydisc in dimension greater than two is not a distance.

For any polynomial f with complex coefficients we find a remarkable subset of poles of the motivic zeta function. It is combinatorially determined by any log resolution and it admits an intrinsic interpretation in terms of contact loci of…

We obtain necessary and sufficient conditions on a function in order that it be the Laplace transform of an absolutely monotonic function. Several closely related results are also given.

We present some completely monotonic functions involving the$q$-polygamma functions, our result generalizes some known results.

We find all matrices $A$ from the spectral unit ball $\Omega_n$ such that the Lempert function $l_{\Omega_n}(A,\cdot)$ is continuous.

We give some further criteria for continuity or discontinuity of the Lempert funtion of the spectral ball $\Omega_n$, with respect to one or both of its arguments, in terms of cyclicity the matrices involved.

In this paper, we present the solution to Kolmogorov's problem for the classes of multiply monotone and completely monotone functions together with its connections to the Markov moment problem, Hermite-Birkhoff interpolation problem, and…

We prove two theorems. Theorem 1 gives the meromorphic continuation of the multiple zeta function to the whole space. In Theorem 2, we prove asymptotic behavior near the non-positive integers.

In the article, a notion "logarithmically absolutely monotonic function" is introduced, an inclusion that a logarithmically absolutely monotonic function is also absolutely monotonic is revealed, the logarithmically complete monotonicity…

We estimate the Lebesgue constants for Lagrange interpolation processes on one or several intervals by rational functions with fixed poles. We admit that the poles have accumulation points on the intervals. To prove it we use an analog of…

We prove one decomposition theorem of complex Monge-Ampere measures of plurisubharmonic functions in connection with their pluripolar sets.

We prove a generalization of classical Montel's theorem for the mixed differences case, for polynomials and exponential polynomial functions, in commutative setting.

For $\Omega$ a domain in $\mathbb C^n$, the pluricomplex Green function with poles $a_1, ...,a_N \in \Omega$ is defined as $G(z):=\sup \{u(z): u\in PSH_-(\Omega), u(x)\le \log \|x-a_j\|+C_j \text{when} x \to a_j, j=1,...,N \}$. When there…

We prove that the set of points where a subharmonic function fails to be continuous is polar.