# Publications of Analysis chair members

Showing search results 1–141 of 141.
2022
• Uncertainty principles with error term in Gelfand-Shilov spaces. (2022). .
• Spherical Logvinenko-Sereda-Kovrijkine type inequality and null-controllability of the heat equation on the sphere. (2022). [arXiv]
• Spectral inequality with sensor sets of decaying density for Schrödinger operators with power growth potentials. (2022). [arXiv]
• The reflection principle in the control problem of the heat equation. (2022). .
• On a minimax principle in spectral gaps. (2022). .
• Uncertainty principle for Hermite functions and null-controllability with sensor sets of decaying density. (2022). [arXiv]
• Control problem for quadratic parabolic differential equations with sensor sets of finite volume or anisotropically decaying density. (2022). [arXiv]
2021
• Unifying the treatment of indefinite and semidefinite perturbations in the subspace perturbation problem. (2021). .
• Wegner Estimate for Random Divergence-Type Operators Monotone in the Randomness. (2021). .
• Protecting points from operator pencils. (2021). .
• An abstract Logvinenko-Sereda type theorem for spectral subspaces. (2021). .
• Uncertainty relations and applications in spectral and control theory. (2021). Oberwolfach Reports.
• Wegner estimate and localisation for alloy type operators with minimal support assumptions on the single site potential. (2021). [arXiv]
• Lifshitz asymptotics and localization for random breather models. (2021). [arXiv]
• The Laplacian on Cartesian products with mixed boundary conditions. (2021). .
• Quantum Hamiltonians with Weak Random Abstract Perturbation. II. Localization in the Expanded Spectrum. (2021). .
2020
• Quantitative unique continuation for spectral subspaces of Schrödinger operators with singular potentials. (2020). [arXiv]
• A minimax principle in spectral gaps. (2020). Appendix to Unique continuation and lifting of spectral band edges of Schrödinger operators on unbounded domains by Ivica Nakić, Matthias Täufer, Martin Tautenhahn and Ivan Veselić. .
• Unique continuation and lifting of spectral band edges of Schrödinger operators on unbounded domains. (2020). With an Appendix by Albrecht Seelmann. .
• Null-controllability and control cost estimates for the heat equation on unbounded and large bounded domains. (2020). In: Control Theory of Infinite-Dimensional Systems, pp. 117–157. Birkhäuser, Cham.
• Exhaustion approximation for the control problem of the heat or Schrödinger semigroup on unbounded domains. (2020). .
• Unique continuation for the gradient of eigenfunctions and Wegner estimates for random divergence-type operators. (2020). [arXiv]
• Uniform Existence of the IDS on Lattices and Groups. (2020). In: Analysis and Geometry on Graphs and Manifolds, pp. 445–478. Cambridge University Press.
• Band edge localization beyond regular Floquet eigenvalues. (2020). .
• The Statistics of Noisy One-Stage Group Testing in Outbreaks. (2020). [arXiv]
• Sharp estimates and homogenization of the control cost of the heat equation on large domains. (2020). .
• Scale-free unique continuation estimates and Logvinenko-Sereda Theorems on the torus. (2020). .
2019
• Sampling and equidistribution theorems for elliptic second order operators, lifting of eigenvalues, and applications. (2019). . [DOI]
• Semidefinite perturbations in the subspace perturbation problem. (2019). .
• Asymptotics of random resonances generated by a point process of delta-interactions. (2019). [arXiv]
• Euler-Lagrange equations for full topology optimization of the Q-factor in leaky cavities. (2019). [arXiv]
• On the multilevel internal structure of the asymptotic distribution of resonances. (2019). . [DOI]
• Geometric conditions for the null-controllability of hypoelliptic quadratic parabolic equations with moving control supports. (2019). [arXiv]
• Concentration inequalities in random Schrödinger operators. (2019). Habilitation thesis, Technische Universität Dortmund.
2018
• Glivenko-Cantelli theory, Ornstein-Weiss quasi-tilings, and uniform ergodic theorems for distribution-valued fields over amenable groups. (2018). .
• Sharp geometric condition for null-controllability of the heat equation on $\Bbb R^d$ and consistent estimates on the control cost. (2018). .
• Spectral localization for quantum Hamiltonians with weak random delta interaction. (2018). . [DOI]
• Scale-free unique continuation principle for spectral projectors, eigenvalue-lifting and Wegner estimates for random Schrödinger operators. (2018). .
• Expansion of the spectrum in the weak disorder regime for random operators in continuum space. (2018). .
• On an estimate in the subspace perturbation problem. (2018). .
• On null-controllability of the heat equation on infinite strips and control cost estimate. (2018). [arXiv]
• On sampling and interpolation by model sets. (2018). submitted. [arXiv]
2017
• Scale-free quantitative unique continuation and equidistribution estimates for solutions of elliptic differential equations. (2017). .
• Lifshitz tails for Schrödinger operators with random breather potential. (2017). .
• A Glivenko-Cantelli theorem for almost additive functions on lattices. (2017). .
• Unique continuation principles and their absence for Schrödinger eigenfunctions on combinatorial and quantum graphs and in continuum space. (2017). .
2016
• Ocean rogue waves and their phase space dynamics in the limit of a linear interference model. (2016). . [DOI]
• Quantum Hamiltonians with weak random abstract perturbation. I. Initial length scale estimate. (2016). .
• Harmonic analysis and random Schrödinger operators. (2016). In: Spectral theory and mathematical physics, pp. 223–255. Birkhäuser, Cham.
• Sampling inequality for $L^2$-norms of eigenfunctions, spectral projectors, and Weyl sequences of Schrödinger operators. (2016). .
• Wegner estimate for Landau-breather Hamiltonians. (2016). .
• A unified approach to convergence rates for $\ell^1$-regularization and lacking sparsity. (2016). .
• Expansion of the almost sure spectrum in the weak disorder regime. (2016). .
• Notes on the subspace perturbation problem for off-diagonal perturbations. (2016). .
• On invariant graph subspaces. (2016). .
2015
• Discrete alloy-type models: regularity of distributions and recent results. (2015). . [arXiv]
• Multiscale unique continuation properties of eigenfunctions. (2015). In: Operator semigroups meet complex analysis, harmonic analysis and mathematical physics, pp. 107–118. Birkhäuser, Cham.
• Conditional Wegner estimate for the standard random breather potential. (2015). .
• Scale-free uncertainty principles and Wegner estimates for random breather potentials. (2015). .
• On $\ell^1$-regularization in light of Nashed's ill-posedness concept. (2015). .
• Wegner estimate and localization for alloy-type models with sign-changing exponentially decaying single-site potentials. (2015). .
• Spectral gap estimates for some block matrices. (2015). .
• Random walks across the sea: the origin of rogue waves?. (2015). [arXiv]
• The length metric on the set of orthogonal projections and new estimates in the subspace perturbation problem. (2015). . [DOI]
• Graph Laplacians do not generate strongly continuous semigroups. (2015). preprint.
• Approximation of the Integrated Density of States on Sofic Groups. (2015). .
2014
• Equidistribution estimates for eigenfunctions and eigenvalue bounds for random operators. (2014). In: Mathematical results in quantum mechanics, pp. 89–99. World Scientific Publishing, Hackensack, NJ.
• Lifshitz asymptotics for percolation Hamiltonians. (2014). .
• Unbounded quantum graphs with unbounded boundary conditions. (2014). .
• Minami's estimate: beyond rank one perturbation and monotonicity. (2014). .
• Notes on the $\sin 2\Theta$ theorem. (2014). .
• Perturbation theory for spectral subspaces. (2014). PhD thesis, Johannes Gutenberg-Universität Mainz. [URL]
• The Anderson model on the Bethe lattice: Lifshitz tails. (2014). preprint. [URL]
2013
• Uniform existence of the integrated density of states for randomly weighted Hamiltonians on long-range percolation graphs. (2013). .
• Low lying eigenvalues of randomly curved quantum waveguides. (2013). .
• Scale-free unique continuation estimates and applications to random Schrödinger operators. (2013). .
• Comment on ''The problem of deficiency indices for discrete Schrödinger operators on locally finite graphs''. (2013). .
2012
• Spectral gaps for self-adjoint second order operators. (2012). .
• Discrete Schrödinger operators with random alloy-type potential. (2012). In: Spectral analysis of quantum Hamiltonians, pp. 107–131. Birkhäuser, Basel.
• Erratum to: A Banach space-valued ergodic theorem and the uniform approximation of the integrated density of states. (2012). .
• Classical motion in random potentials. (2012). .
2011
• Anderson localization for a class of models with a sign-indefinite single-site potential via fractional moment method. (2011). .
• Generalized eigenfunctions and spectral theory for strongly local Dirichlet forms. (2011). In: Spectral theory and analysis, pp. 83–106. Springer, Basel.
• Lipschitz-continuity of the integrated density of states for Gaussian random potentials. (2011). .
• $L^p$-approximation of the integrated density of states for Schrödinger operators with finite local complexity. (2011). .
• A Banach space-valued ergodic theorem and the uniform approximation of the integrated density of states. (2011). .
• Low lying spectrum of weak-disorder quantum waveguides. (2011). .
• Quantitative unique continuation principle and Wegner estimates (on joint work with C. Rojas-Molina). (2011). . [DOI]
• The problem of deficiency indices for discrete Schrödinger operators on locally finite graphs. (2011). .
2010
• Wegner estimates for sign-changing single site potentials. (2010). .
• Localization via fractional moments for models on $\Bbb Z$ with single-site potentials of finite support. (2010). .
• Wegner estimate for discrete alloy-type models. (2010). .
• Spectral properties of discrete alloy-type models. (2010). In: XVIth International Congress on Mathematical Physics, pp. 551–555. World Scientific Publishing, Hackensack, NJ.
• Lifshitz tails for a class of Schrödinger operators with random breather-type potential. (2010). .
• Metric properties of the set of orthogonal projections and their applications to operator perturbation theory. (2010). [arXiv]
• Klassische Bewegung in zufälligen Potentialen mit Coulomb-Singularitäten. (2010). PhD thesis, FAU Erlangen/Nürnberg. [URL]
2009
• Spectral asymptotics of percolation Hamiltonians on amenable Cayley graphs. (2009). In: Methods of spectral analysis in mathematical physics, pp. 1–29. Birkhäuser, Basel.
• Equality of Lifshitz and van Hove exponents on amenable Cayley graphs. (2009). .
• Hamiltonians on discrete structures: jumps of the integrated density of states and uniform convergence. (2009). .
• Continuity of the integrated density of states on random length metric graphs. (2009). .
• The Allegretto-Piepenbrink theorem for strongly local Dirichlet forms. (2009). . [arXiv]
• Wegner-type bound for discrete alloy-type models. (2009). . [DOI]
• Mini-Workshop: Modeling and Understanding Random Hamiltonians: Beyond Monotonicity, Linearity and Independence. (2009). . [DOI]
2008
• Optimal Wegner estimates for random Schrödinger operators on metric graphs. (2008). In: Analysis on graphs and its applications, pp. 409–422. American Mathematical Society, Providence, RI.
• Uniform existence of the integrated density of states for combinatorial and metric graphs over $\Bbb Z^d$. (2008). In: Analysis on graphs and its applications, pp. 87–108. American Mathematical Society, Providence, RI.
• Uniform existence of the integrated density of states for models on $\Bbb Z^d$. (2008). .
• The modulus of continuity of Wegner estimates for random Schrödinger operators on metric graphs. (2008). .
• Continuity properties of the integrated density of states on manifolds. (2008). .
• Sharpness of the phase transition and exponential decay of the subcritical cluster size for percolation and quasi-transitive graphs. (2008). .
• Existence and regularity properties of the integrated density of states of random Schrödinger Operators. (2008). Revised version of the habilitation thesis. Springer, Berlin and Heidelberg. [DOI]
• Wegner estimates for non-monotoneously correlated alloy type models. (2008). . [DOI]
• Quanten-Kodierungstheorie und kodierte Operationen am Beispiel der Quanten-Fouriertransformation. (2008). Diploma thesis, Johannes Gutenberg-Universität Mainz.
2007
• Uniform existence of the integrated density of states for random Schrödinger operators on metric graphs over $\Bbb Z^d$. (2007). .
• Linear Wegner estimate for alloy-type Schrödinger operators on metric graphs. (2007). .
• Groupoids, von Neumann algebras and the integrated density of states. (2007). .
• Lower bounds on the lowest spectral gap of singular potential Hamiltonians. (2007). .
• Spectral gap of segments of periodic waveguides. (2007). .
• Lifshitz asymptotics for Hamiltonians monotone in the randomness. (2007). .
• Mini-Workshop: Multiscale and Variational Methods in Material Science and Quantum Theory of Solids. (2007). . [DOI]
2006
• Existence and regularity properties of the integrated density of states of random Schrödinger Operators. (2006). Habilitation thesis, Technische Universität Chemnitz. [URL]
• On the Lipschitz continuity of the integrated density of states for sign-indefinite potentials. (2006). .
• Bounds on the spectral shift function and the density of states. (2006). .
• Spectral properties of Anderson-percolation Hamiltonians. (2006). .
• Mini-Workshop: $L^2$-Spectral Invariants and the Integrated Density of States. (2006). . [DOI]
2005
• Spectral analysis of percolation Hamiltonians. (2005). .
• Quantum site percolation on amenable graphs. (2005). In: Proceedings of the Conference on Applied Mathematics and Scientific Computing, pp. 317–328. Springer, Dordrecht.
2004
• Integrated density of states and Wegner estimates for random Schrödinger operators. (2004). In: Spectral theory of Schrödinger operators, pp. 97–183. American Mathematical Society, Providence, RI.
• Integrated density of states for random metrics on manifolds. (2004). .
• Bound on the spectral shift function and the (integrated) density of states. (2004). . [DOI]
• Klassische Bewegung in zufälligen Potentialen. (2004). Diploma thesis, FAU Erlangen/Nürnberg.
2003
• Random Schrödinger operators on manifolds. (2003). . [arXiv]
• Existence of the density of states for some alloy type models with single site potentials that change sign. (2003). In: Applied mathematics and scientific computing, pp. 301–311. Springer, Boston, MA.
2002
• Wegner estimate for indefinite Anderson potentials: some recent results and applications. (2002). . [arXiv]
• Existence of the density of states for one-dimensional alloy-type potentials with small support. (2002). In: Mathematical results in quantum mechanics, pp. 171–176. American Mathematical Society, Providence, RI.
• Integrated density of states for ergodic random Schrödinger operators on manifolds. (2002). .
• Localization for random perturbations of periodic Schrödinger operators with regular Floquet eigenvalues. (2002). .
• Wegner estimate and the density of states of some indefinite alloy-type Schrödinger operators. (2002). .
• Wegner estimate for sparse and other generalized alloy type potentials. (2002). . [DOI]
2001
• Indefinite Probleme bei der Anderson-Lokalisierung. (2001). PhD thesis, Ruhr-Universität Bochum. [URL]
2000
• Integrated density of states for random Schrödinger operators on manifolds. (2000). MaPhySto research report. [URL]
1996
• Lokalisierung bei zufällig gestörten periodischen Schrödingeroperatoren in Dimension Eins. (1996). Diploma thesis, Ruhr-Universität Bochum. [URL]

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