Preprints
- Recurrent and (strongly) resolvable graphs (arXivExterner Link) (with Daniel Lenz, Simon Pucher), submitted, 36pp.
- Boundary representations of intermediate forms between a regular Dirichlet form and its active main part (arXivExterner Link) (with Matthias Keller, Daniel Lenz, Michael Schwarz, Melchior Wirth), submitted, 24pp.
- Blow-up of nonnegative solutions of an abstract semilinear heat equation with convex source (arXivExterner Link) (with Daniel Lenz, Ian Zimmermann), submitted, 16pp.
- Topological Poincaré type inequalities and lower bounds on the infimum of the spectrum for graphs (arXivExterner Link) (with Daniel Lenz, Peter Stollmann), submitted, 23pp.
- Geometric properties of Dirichlet forms under order isomorphisms (arXivExterner Link) (with Daniel Lenz, Melchior Wirth), submitted, 30pp.
Publications
- (Weak) Hardy and Poincaré inequalities and criticality theory (journal,Externer Link arXivExterner Link) Dirichlet forms and related topics, 421–459, Springer Proc. Math. Stat., 394, Springer, Singapore, [2022].
- On Lp Liouville theorems for Dirichlet forms (journalExterner Link, arXivExterner Link) (with Bobo Hua, Matthias Keller, Daniel Lenz), Dirichlet forms and related topics, 201-221, Springer Proc. Math. Stat., 394, Springer, Singapore, [2022].
- Uniqueness of form extensions and domination of semigroups (journalExterner Link, arXivExterner Link)
(with Daniel Lenz, Melchior Wirth), J. Funct. Anal. 280 (2021), no. 6,, 27 pp. - On the uniqueness class, stochastic completeness and volume growth for graphs (journal,Externer LinkarXivExterner Link) (with Xueping Huang, Matthias Keller), Trans. Amer. Math. Soc. 373 (2020), no. 12, 8861-8884.
- On the existence and uniqueness of self-adjoint realizations of discrete (magnetic) Schrödinger operators (journal,Externer LinkarXivExterner Link) in Analysis and Geometry on Graphs and Manifolds, 250 - 327, eds. Matthias Keller, Daniel Lenz, Radoslaw Wojciechowski, London Mathematical Society Lecture Note Series, 461. Cambridge University Press, Cambridge, 2020.
- A note on the surjectivity of operators on vector bundles over discrete spaces (journal,Externer LinkarXivExterner Link) (with Jannis Koberstein), Arch. Math. (Basel) 114 (2020), no. 3, 313-329.
- Domination of quadratic forms (journal,Externer LinkarXivExterner Link) (with Daniel Lenz, Melchior Wirth), to appear in Math. Z., 24pp.
- A generalized conservation property for the heat semigroup on weighted manifolds (journalExterner Link, arXivExterner Link)(with Jun Masamune), Math. Ann. 377 (2020), no. 3-4, 1673-1710.
- A note on reflected Dirichlet forms (journalExterner Link, arXivExterner Link) Potential Anal. 52 (2020), no. 2, 245-279.
- Boundary representation of Dirichlet forms on discrete spaces (journalExterner Link, arXivExterner Link) (with Matthias Keller, Daniel Lenz, Michael Schwarz), J. Math. Pures Appl. (9) 126 (2019), 109-143.
- The Ihara Zeta function for infinite graphs (journalExterner Link, arXivExterner Link) (with Daniel Lenz, Felix Pogorzelski), Trans. Amer. Math. Soc. 371 (2019), no. 8, 5687-5729.
- Global properties of Dirichlet forms in terms of Green's formula (journalExterner Link, arXivExterner Link) (with Sebastian Haeseler, Matthias Keller, Daniel Lenz, Jun Masamune), Calc. Var. Partial Differential Equations 56 (2017), no. 5, Art. 124, 43 pp.
- Global properties of Dirichlet forms on discrete spaces (journalExterner Link, arXivExterner Link) (based on my Diploma thesis) Dissertationes Math. (Rozprawy Mat.) 522 (2017), 1-43.
- Note on short time behavior of semigroups associated to selfadjoint operators (journalExterner Link, arXivExterner Link) (with Matthias Keller, Daniel Lenz, Florentin Münch, Andras Telcs), Bull London Math Soc (2016) 48 (6): 935-944.
- Note on uniformly transient graphs (journalExterner Link, arXivExterner Link) (with Matthias Keller, Daniel Lenz, Radoslaw Wojciechowski), Rev. Mat. Iberoam. 33 (2017), no. 3, 831-860.
- A Feynman-Kac-Ito Formula for magnetic Schrödinger operators on graphs (journalExterner Link, arXivExterner Link) (with Batu Güneysu, Matthias Keller), Probability Theory and Related Fields, 165 (2016), no. 1-2, 365-399.
- Diffusion determines the recurrent graph (journalExterner Link, arXivExterner Link) (with Matthias Keller, Daniel Lenz, Melchior Wirth), Advances in Mathematics, Volume 269 (2015), 364-398.
PhD thesis
- Energy forms (arXivExterner Link), 196pp.
Diploma thesis
- Global properties of Dirichlet forms on discrete spaces (arXivExterner Link), 49pp.