R. Pruckner

activity

20152023

most citedCanonical systems whose Weyl coefficients have regularly varying asymptotics

2 citations · 2 across the 6 of their papers we have counts for

collaborators

8 papers

math.CA2023

An upper bound for the Nevanlinna matrix of an indeterminate moment sequence

Raphael Pruckner, Jakob Reiffenstein, Harald Woracek

The solutions of an indeterminate Hamburger moment problem can be parameterised using the Nevanlinna matrix of the problem. The entries of this matrix are entire functions of minim…

math.SP2022

A growth estimate for the monodromy matrix of a canonical system

Raphael Pruckner, Harald Woracek

We investigate the spectrum of 2-dimensional canonical systems in the limit circle case. It is discrete and, by the Krein-de Branges formula, cannot be more dense than the integers…

math.SP2022★ 2 cited

Canonical systems whose Weyl coefficients have regularly varying asymptotics

Matthias Langer, Raphael Pruckner, Harald Woracek

For a two-dimensional canonical system $y^{'} (t) = z J H (t) y (t)$ on an interval $(0, L)$ with $0 < L \leq \infty$ whose Hamiltonian $H$ is a.e.\ positive semidefinite, denote by $q_{H}$ its Weyl…

math.SP2021

Canonical systems whose Weyl coefficients have dominating real part

Matthias Langer, Raphael Pruckner, Harald Woracek

For a two-dimensional canonical system $y^{'} (t) = z J H (t) y (t)$ on the half-line $(0, \infty)$ whose Hamiltonian $H$ is a.e. positive semi-definite, denote by $q_{H}$ its Weyl coefficient.…

math.FA2021

Limit behaviour of Weyl coefficients

Raphael Pruckner, Harald Woracek

We study the sets of radial or nontangential limit points towards $i \infty$ of a Nevanlinna function q. Given a nonempty, closed, and connected subset L of $C_{+}$ , we explicitly co…

math-ph2021

Estimates for the Weyl coefficient of a two-dimensional canonical system

Matthias Langer, Raphael Pruckner, Harald Woracek

For a two-dimensional canonical system $y^{'} (t) = z J H (t) y (t)$ on some interval $(a, b)$ whose Hamiltonian $H$ is a.e. positive semi-definite and which is regular at $a$ and in the limit…

math.SP2017

Density of the spectrum of Jacobi matrices with power asymptotics

Raphael Pruckner

We consider Jacobi matrices $J$ whose parameters have the power asymptotics $ρ_{n} = n^{β_{1}} (x_{0} + \frac{x _{1}}{n} + O (n^{- 1 - ε}))$ and $q_n=n^{β_2} \left( y_0 + \frac{…

math.SP2015

Bounds on order of indeterminate moment sequences

Raphael Pruckner, Roman Romanov, Harald Woracek

We investigate the order $ρ$ of the four entire functions in the Nevanlinna matrix of an indeterminate Hamburger moment sequence. We give an upper estimate for $ρ$ which is explici…