# Research articles

## Preprint articles

• Boundary Harnack inequality for Markov processes with jumps with Krzysztof Bogdan and Takashi Kumagai, to appear in Trans. Amer. Math. Soc. [arXiv]

## Publications

• Estimates and structure of α-harmonic functions with Krzysztof Bogdan and Tadeusz Kulczycki, Prob. Theory Rel. Fields 140(3–4) (2008): 345–381 [online]
• Spectral gap estimate for stable processes on arbitrary bounded open sets, Probab. Math. Statist. 28(1) (2008): 163–167 [online]
• Intrinsic ultracontractivity for stable semigroups on unbounded open sets, Potential Anal. 31(1) (2009): 57–77 [online]
• Eigenvalues of the Cauchy process on an interval have at most double multiplicity, Semigroup Forum 79(1) (2009): 183–192 [online]
• Spectral properties of the Cauchy process on half-line and interval with Tadeusz Kulczycki, Jacek Małecki and Andrzej Stós, Proc. London Math. Soc. 101(2) (2010): 589–622 [online]
• Boundary Harnack inequality for α-harmonic functions on the Sierpiński triangle with Kamil Kaleta, Probab. Math. Stat. 30(2) (2010): 353–368 [online]
• Spectral analysis of subordinate Brownian motions on the half-line, Studia Math. 206(3) (2011): 211–271 [online]
• Eigenvalues of the fractional Laplace operator in the interval, J. Funct. Anal. 262(5) (2012): 2379–2402 [online]
• Spectral theory for one-dimensional symmetric Lévy processes killed upon hitting the origin, Electron. J. Probab. 17 (2012), no. 83 [online]
• On high spots of the fundamental sloshing eigenfunctions in axially symmetric domains (with Tadeusz Kulczycki), Proc. London Math. Soc. 105(5) (2012): 921–952 [online]
• First passage times for subordinate Brownian motions with Jacek Małecki and Michał Ryznar, Stoch. Proc. Appl 123 (2013): 1820–1850 [online]
Note: In Sect. 1 every occurrence of $2 \xi \Psi''(\xi) \le \Psi'(\xi)$ should be $\xi \Psi''(\xi) \le \Psi'(\xi)$ (5 times).
• Suprema of Lévy processes with Jacek Małecki and Michał Ryznar, Ann. Probab. 41(3B) (2013): 2047–2065 [online]
• One-dimensional quasi-relativistic particle in the box with Kamil Kaleta and Jacek Małecki, Rev. Math. Phys. 25(8) 1350014 [online]

## Selected conference presentations

• Rogers functions and fluctuation theory [pdf]
7th Conference on Lévy Processes (Wrocław, Poland, 2013)
• Recent progress in the study of suprema of Lévy processes [pdf]
German–Polish Conference on Probability and Mathematical Statistics (Toruń, Poland, 2013)
• Two-term asymptotics for Lévy operators in intervals [pdf]
6nd International Conference on Stochastic Analysis and Its Applications (Będlewo, Poland, 2012)
• Spectral decomposition of integro-differential operators related to one-dimensional Lévy processes in domains [pdf]
Harmonic Analysis and Probability (Angers, France, 2012)
• Boundary Harnack Inequality For Jump-Type Processes [pdf]
Foundations of Stochastic Analysis (Banff, Canada, 2011)
• Spectral Theory for Subordinate Brownian Motions in Half-line [pdf]
Yangyang Summer School (Yangyang, Korea, 2011)
• Cauchy process on half-line [pdf]
3rd International Conference on Stochastic Analysis and Its Applications (Beijing, China, 2009)
• Boundary Harnack inequality for stable processes on the Sierpiński gasket [pdf]
Fractal Geometry and Stochastics 4 (Greifswald, Germany, 2008)
• Intrinsic ultracontractivity for isotropic stable processes in unbounded domains [pdf]
2nd International Conference on Stochastic Analysis and Its Applications (Seoul, Korea, 2008)