14 citations · 33 across the 17 of their papers we have counts for
23 papers
Strict Wick-type deformation quantization on Riemann surfaces: Rigidity and Obstructions
Daniela Kraus, Oliver Roth, Sebastian Schleissinger +1
Let be a hyperbolic Riemann surface. We study a convergent Wick-type star product on which is induced by the canonical convergent star product $\star_{\mathbb{D}}…
Nonlinear resolvents and decreasing Loewner chains
Ikkei Hotta, Sebastian Schleißinger, Toshiyuki Sugawa
In this article we prove that nonlinear resolvents of infinitesimal generators on bounded and convex subdomains of $\C^n$ are decreasing Loewner chains. Furthermore, we consider th…
A quantum invitation to probability theory
Sebastian Schleißinger
Quantum probability theory and complex analysis for children.
Limits of radial multiple SLE and a Burgers-Loewner differential equation
Ikkei Hotta, Sebastian Schleißinger
We consider multiple radial SLE as the number of curves tends to infinity. We give conditions that imply the tightness of the associated processes given by the Loewner equation. In…
Problems related to conformal slit-mappings
Ikkei Hotta, Sebastian Schleißinger
In this note we discuss some problems related to conformal slit-mappings. On the one hand, classical Loewner theory leads us to questions concerning the embedding of univalent func…
A quantum remark on biholomorphic mappings on the unit ball
Sebastian Schleißinger
In this note we regard non-commutative probability theory with operator-valued expectation. We show that the moment generating functions of distributions coming from monotone incre…
Monotone Increment Processes, Classical Markov Processes, and Loewner Chains
Uwe Franz, Takahiro Hasebe, Sebastian Schleißinger
We prove one-to-one correspondences between certain decreasing Loewner chains in the upper half-plane, a special class of real-valued Markov processes, and quantum stochastic proce…
Loewner's Differential Equation and Spidernets
Sebastian Schleißinger
We regard a certain type of Loewner's differential equation from a quantum probability point of view and approximate the underlying quantum process by the adjacency matrices of gro…
On the parametric representation of univalent functions on the polydisc
Sebastian Schleißinger
We consider support points of the class of normalized univalent mappings on the polydisc with parametric representation and we prove sharp estima…
Approximation properties of univalent mappings on the unit ball in
Hidetaka Hamada, Mihai Iancu, Gabriela Kohr +1
Let . In this paper, we obtain approximation properties of various families of normalized univalent mappings on the Euclidean unit ball in $\mathbb{C}^n…
Tightness results for infinite-slit limits of the chordal Loewner equation
Andrea del Monaco, Ikkei Hotta, Sebastian Schleißinger
In this note we consider a multi-slit Loewner equation with constant coefficients that describes the growth of multiple SLE curves connecting points on to infinity…
The Chordal Loewner Equation and Monotone Probability Theory
Sebastian Schleißinger
In [5], O. Bauer interpreted the chordal Loewner equation in terms of non-commutative probability theory. We follow this perspective and identify the chordal Loewner equations as t…
Three Value Ranges for Symmetric Self-mappings
Julia Koch, Sebastian Schleißinger
Let be the unit disc and We determine the value range , where is the set of holomorphic fun…
Value Ranges of Univalent Self-Mappings of the Unit Disc
Julia Koch, Sebastian Schleissinger
We describe the value set where denotes the unit disc and $z_0\in\mathbb{D}\setm…
Multiple SLE and the complex Burgers equation
Andrea del Monaco, Sebastian Schleissinger
In this paper we ask whether one can take the limit of multiple SLE as the number of slits goes to infinity. In the special case of slits that connect points of the boundar…
Chordal generators and the hydrodynamic normalization for the unit ball
Sebastian Schleissinger
Let and denote by the set of all infinitesimal generators on the upper half-plane such that $\limsup_{…
Embedding Problems in Loewner Theory
Sebastian Schleissinger
In part 1 (Chapter 2) we present the basic notions of Loewner theory. Here we use a modern form which was developed by F. Bracci, M. Contreras, S. Díaz-Madrigal et al. and which ca…
On driving functions generating quasislits in the chordal Loewner-Kufarev equation
Sebastian Schleissinger
We prove that for every there exists a driving function such that the corresponding chordal Loewner-Kufarev equation generates a quasislit and $ \limsu…
The Loewner Equation for Multiple Slits, Multiply Connected Domains and Branch Points
Christoph Böhm, Sebastian Schleißinger
Let be parametrizations of two slits such that and are disjoint. \\ Let to be t…
Constant Coefficients in the Radial Komatu-Loewner Equation for Multiple Slits
Christoph Böhm, Sebastian Schleißinger
The radial Komatu-Loewner equation is a differential equation for certain normalized conformal mappings that can be used to describe the growth of slits within multiply connected d…
Rogosinski's lemma for univalent functions, hyperbolic Archimedean spirals and the Loewner equation
Oliver Roth, Sebastian Schleißinger
We describe the region of values of for all normalized bounded univalent functions in the unit disk at a fixed point $z_0 \in \mathbb{D…
The Schramm-Loewner equation for multiple slits
Oliver Roth, Sebastian Schleißinger
We prove that any disjoint union of finitely many simple curves in the upper half-plane can be generated in a unique way by the chordal multiple-slit Loewner equation with constant…
The multiple-slit version of Loewner's differential equation and pointwise Hölder continuity of driving functions
Sebastian Schleißinger
We consider the chordal Loewner differential equation for multiple slits in the upper half-plane and relations between the pointwise Hölder continuity of the driving functions and…