Related papers: The Multivariate Herglotz-Nevanlinna Class: Superr…
We establish new analytic and numerical results on a general class of rational operator Nevanlinna functions that arise e.g. in modelling photonic crystals. The capability of these dielectric nano-structured materials to control the flow of…
The class of differential-equation eigenvalue problems $-y''(x)+x^{2N+2}y(x)=x^N Ey(x)$ ($N=-1,0,1,2,3,...$) on the interval $-\infty<x<\infty$ can be solved in closed form for all the eigenvalues $E$ and the corresponding eigenfunctions…
The H\"older continuity of the truncated moment map of a shade function in Euclidean space is established in the vicinity of a principal semi-algebraic set. The proof combines volume bounds of semi-algebraic sets and convex optimization…
Additional integral inequalities are obtained for integrals of the differences of subharmonic functions by Borel measures on balls in a multidimensional Euclidean space. These integrals are still estimated from above through the Nevanlinna…
We study non-univalent solutions of the Polubarinova-Galin equation, describing the time evolution of the conformal map from the unit disk onto a Hele-Shaw blob of fluid subject to injection at one point. In particular, we tackle the…
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…
Biunivalent holomorphic functions form an interesting class in geometric function theory and are connected with special functions and solutions of complex differential equations. The paper reveals a deep connection between biunivalence and…
We propose a symbolic-numeric algorithm to count the number of solutions of a polynomial system within a local region. More specifically, given a zero-dimensional system $f_1=\cdots=f_n=0$, with $f_i\in\mathbb{C}[x_1,\ldots,x_n]$, and a…
We present the applications of variation -- wavelet analysis to polynomial/rational approximations for orbital motion in transverse plane for a single particle in a circular magnetic lattice in case when we take into account multipolar…
We generalize two integral representation formulae of Nevanlinna to functions of several variables. We show that for a large class of analytic functions that have non-negative imaginary part on the upper polyhalfplane there are…
We establish existence of positive non-decreasing radial solutions for a nonlocal nonlinear Neumann problem both in the ball and in the annulus. The nonlinearity that we consider is rather general, allowing for supercritical growth (in the…
We solve a three point Nevanlinna-Pick problem in the Euclidean ball. In particular, we determine a class of rational functions that interpolate this problem.
We extend the univariate Newton interpolation algorithm to arbitrary spatial dimensions and for any choice of downward-closed polynomial space, while preserving its quadratic runtime and linear storage cost. The generalisation supports any…
In this paper, we give several characterizations of Herglotz-Nevanlinna functions in terms of a specific type of positive semi-definite functions called Poisson-type functions. This allows us to propose a multidimensional analogue of the…
A seminal result of Agler characterizes the so-called Schur-Agler class of functions on the polydisk in terms of a unitary colligation transfer function representation. We generalize this to the unit ball of the algebra of multipliers for a…
In this study, we derive the sharp bounds of certain Toeplitz determinants whose entries are the coefficients of holomorphic functions belonging to a class defined on the unit disk $\mathbb{U}$. Further, these results are extended to a…
We develop an analysis of wavelets and pseudodifferential operators on multidimensional ultrametric spaces which are defined as products of locally compact ultrametric spaces. We introduce bases of wavelets, spaces of generalized functions…
The study is made of the problem of multiple interpolation on an infinite nodes set by the sums of absolutely convergent series of exponentials whose exponents are from a given set. For entire function conditions on nodes and exponents are…
Considering a finite intersection of balls and a finite union of other balls in an Euclidean space, we propose an exact method to test whether the intersection is covered by the union. We reformulate this problem into quadratic programming…
This paper analyzes the structure of the set of nodal solutions of a class of one-dimensional superlinear indefinite boundary values problems with an indefinite weight functions in front of the spectral parameter. Quite astonishingly, the…