Browsing by Autor "Monika Winklmeier"

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A spectral approach to the Dirac equation in the non-extreme Kerr–Newmann metric
(Institute of Physics, 2009) Monika Winklmeier; Osanobu Yamada
We investigate the local energy decay of solutions of the Dirac equation in the non-extreme Kerr–Newman metric. First, we write the Dirac equation as a Cauchy problem and define the Dirac operator. It is shown that the Dirac operator is selfadjoint in a suitable Hilbert space. With the RAGE theorem, we show that for each particle its energy located in any compact region outside the event horizon of the Kerr–Newman black hole decays in the time mean.
On the Density of Certain Languages with $p^2$ Letters
(Electronic Journal of Combinatorics, 2015) Carlos Segovia; Monika Winklmeier
The sequence $(x_n)_{n\in\mathbb N} = (2,5,15,51,187,\ldots)$ given by the rule $x_n=(2^n+1)(2^{n-1}+1)/3$ appears in several seemingly unrelated areas of mathematics. For example, $x_n$ is the density of a language of words of length $n$ with four different letters. It is also the cardinality of the quotient of $(\mathbb Z_2\times \mathbb Z_2)^n$ under the left action of the special linear group $\mathrm{SL}(2,\mathbb Z)$. In this paper we show how these two interpretations of $x_n$ are related to each other. More generally, for prime numbers $p$ we show a correspondence between a quotient of $(\mathbb Z_p\times\mathbb Z_p)^n$ and a language with $p^2$ letters and words of length $n$.
Spectral inclusions of perturbed normal operators and applications
(Cambridge University Press, 2026) Javier Moreno; Monika Winklmeier
Abstract We consider a normal operator $T$ on a Hilbert space $H$ . Under various assumptions on the spectrum of $T$ , we give bounds for the spectrum of $T+A$ where $A$ is $T$ -bounded with relative bound less than 1 but we do not assume that $A$ is symmetric or normal. If the imaginary part of the spectrum of $T$ is bounded, then the spectrum of $T+A$ is contained in the region between two hyperbolas whose asymptotic slope depends on the $T$ -bound of $A$ . If the spectrum of $T$ is contained in a bisector, then the spectrum of $T+A$ is contained in the area between certain rotated hyperbolas. The case of infinitely many gaps in the spectrum of $T$ is studied. Moreover, we prove a stability result for the essential spectrum of $T+A$ . If $A$ is even $p$ -subordinate to $T$ , then we obtain stronger results for the localisation of the spectrum of $T+A$ .