## Mateusz Kwaśnicki

Department of Pure Mathematics
Wrocław University of Science and Technology
ul. Wybrzeże Wyspiańskiego 27
50-370 Wrocław, Poland

e-mail:
skype: mateusz.kwasnicki
ORCID: 0000-0003-3896-8124

# Research articles

For an author's copy of any of the following papers, please send me an email at .

## Preprint articles

• Andreas E. Kyprianou, Mateusz Kwaśnicki, Sandra Palau and Tsogzolmaa Saizmaa, Oscillatory attraction and repulsion from a subset of the unit sphere or hyperplane for isotropic stable Lévy processes [arXiv]
• Mateusz Kwaśnicki, Boundary traces of shift-invariant diffusions in half-plane [arXiv]
• Mateusz Kwaśnicki, Thomas Simon, Characterisation of the class of bell-shaped functions [arXiv]
• Mateusz Kwaśnicki, Harmonic extension technique for non-symmetric operators with completely monotone kernels [arXiv]

## Publications

1. Mateusz Kwaśnicki, Random walks are determined by their trace on the positive half-line, Ann. Henri Lebesgue 3 (2020): 1389–1397 [online|MR|zb]
2. Mateusz Kwaśnicki, A new class of bell-shaped functions, Trans. Amer. Math. Soc. 373(4) (2020): 2255–2280 [online|MR|zb]
3. Alexey Kuznetsov, Mateusz Kwaśnicki, Minimal Hermite-type eigenbasis of the discrete Fourier transform, J. Fourier Anal. Appl. 25(3) (2019): 1053–1079 [online|MR|zb]
4. Mateusz Kwaśnicki, Fluctuation theory for Lévy processes with completely monotone jumps, Electron. J. Probab. 24 (2019), no. 40 [online|MR|zb]
(supersedes: Rogers functions and fluctuation theory [arXiv])
5. Rodrigo Bañuelos, Mateusz Kwaśnicki, On the $\ell^p$ norm of the discrete Hilbert transform, Duke Math. J. 168(3) (2019): 471–504 [online|MR|zb]
6. Mateusz Kwaśnicki, Richard S. Laugesen, Bartłomiej Siudeja Pólya’s conjecture fails for the fractional Laplacian, J. Spectral Theory 9(1) (2019): 127–135 [online|MR|zb]
7. Mateusz Kwaśnicki, Fractional Laplace Operator and its Properties, in: A. Kochubei, Y. Luchko, Handbook of Fractional Calculus with Applications. Volume 1: Basic Theory, De Gruyter Reference, De Gruyter, Berlin, 2019 [online|MR|google]
8. Mateusz Kwaśnicki, Jacek Mucha, Extension technique for complete Bernstein functions of the Laplace operator, J. Evol. Equ. 18(3) (2018): 1341–1379 [online|MR|zb]
9. Alexey Kuznetsov, Mateusz Kwaśnicki, Spectral analysis of stable processes on the positive half-line, Electron. J. Probab. 23 (2018), no. 10 [online|MR|zb]
10. Kamil Kaleta, Mateusz Kwaśnicki, József Lőrinczi, Contractivity and ground state domination properties for non-local Schrödinger operators, J. Spectr. Theory 8 (2018): 165–189 [online|MR|zb]
11. Tomasz Grzywny, Mateusz Kwaśnicki, Potential kernels, probabilities of hitting a ball, harmonic functions and the boundary Harnack inequality for unimodal Lévy processes, Stoch. Proc. Appl. 128(1) (2018): 1–38 [online|MR|zb]
12. Tomasz Juszczyszyn, Mateusz Kwaśnicki, Martin kernels for Markov processes with jumps, Potential Anal. 47(3) (2017): 313–335 [online|MR|zb]
13. Bartłomiej Dyda, Alexey Kuznetsov, Mateusz Kwaśnicki, Eigenvalues of the fractional Laplace operator in the unit ball, J. London Math. Soc. 95 (2017): 500–518 [online|MR|zb]
14. Bartłomiej Dyda, Alexey Kuznetsov, Mateusz Kwaśnicki, Fractional Laplace operator and Meijer G-function, Constructive Approx. 45(3) (2017): 427–448 [online|MR|zb]
15. Mateusz Kwaśnicki, Ten equivalent definitions of the fractional Laplace operator, Frac. Calc. Appl. Anal. 20(1) (2017): 7–51 [online|MR|zb]
Note: $p \in (1, \infty)$ should read $p \in (1, \tfrac{d}{\alpha})$ in page 22, line 20.
16. Kamil Kaleta, Mateusz Kwaśnicki, Jacek Małecki, Asymptotic estimate of eigenvalues of pseudo-differential operators in an interval, J. Math. Anal. Appl. 439(2) (2016): 896–924 [online|MR|zb]
17. Tadeusz Kulczycki, Mateusz Kwaśnicki, Bartłomiej Siudeja, The shape of the fundamental sloshing mode in axisymmetric containers, J. Eng. Math. 99(1) (2015): 157–183 [online|MR|zb]
18. Tomasz Juszczyszyn, Mateusz Kwaśnicki, Hitting times of points for symmetric Lévy processes with completely monotone jumps, Electron. J. Probab. 20 (2015), no. 48 [online|MR|zb]
19. Krzysztof Bogdan, Takashi Kumagai, Mateusz Kwaśnicki, Boundary Harnack inequality for Markov processes with jumps, Trans. Amer. Math. Soc. 367(1) (2015): 477–517 [online|MR|zb]
20. James Burridge, Alexey Kuznetsov, Andreas Kyprianou, Mateusz Kwaśnicki, New families of subordinators with explicit transition probability semigroup, Stoch. Proc. Appl. 124(10) (2014): 3480–3495 [online|MR|zb]
21. Nikolay Kuznetsov, Tadeusz Kulczycki, Mateusz Kwaśnicki, Alexander Nazarov, Sergey Poborchi, Iosif Polterovich and Bartłomiej Siudeja, The Legacy of Vladimir Andreevich Steklov, Notices Amer. Math. Soc. 61(1) (2014): 9–23 [online|MR|zb]
22. Kamil Kaleta, Mateusz Kwaśnicki, Jacek Małecki, One-dimensional quasi-relativistic particle in the box, Rev. Math. Phys. 25(8) (2013) 1350014 [online|MR|zb]
Note: In the first displayed formula in Lemma~4.2 the norm in the left-hand side should not be squared.
23. Mateusz Kwaśnicki, Jacek Małecki, Michał Ryznar, Suprema of Lévy processes, Ann. Probab. 41(3B) (2013): 2047–2065 [online|MR|zb]
24. Mateusz Kwaśnicki, Jacek Małecki, Michał Ryznar, First passage times for subordinate Brownian motions, Stoch. Proc. Appl. 123 (2013): 1820–1850 [online|MR|zb]
25. Mateusz Kwaśnicki, Tadeusz Kulczycki, On high spots of the fundamental sloshing eigenfunctions in axially symmetric domains, Proc. London Math. Soc. 105(5) (2012): 921–952 [online|MR|zb]
26. Mateusz Kwaśnicki, Spectral theory for one-dimensional symmetric Lévy processes killed upon hitting the origin, Electron. J. Probab. 17 (2012), no. 83 [online|MR|zb]
27. Mateusz Kwaśnicki, Eigenvalues of the fractional Laplace operator in the interval, J. Funct. Anal. 262(5) (2012): 2379–2402 [online|MR|zb]
28. Mateusz Kwaśnicki, Spectral analysis of subordinate Brownian motions on the half-line, Studia Math. 206(3) (2011): 211–271 [online|MR|zb]
29. Kamil Kaleta, Mateusz Kwaśnicki, Boundary Harnack inequality for α-harmonic functions on the Sierpiński triangle, Probab. Math. Stat. 30(2) (2010): 353–368 [online|MR|zb]
30. Tadeusz Kulczycki, Mateusz Kwaśnicki, Jacek Małecki and Andrzej Stós, Spectral properties of the Cauchy process on half-line and interval, Proc. London Math. Soc. 101(2) (2010): 589–622 [online|MR|zb]
31. Mateusz Kwaśnicki, Eigenvalues of the Cauchy process on an interval have at most double multiplicity, Semigroup Forum 79(1) (2009): 183–192 [online|MR|zb]
32. Mateusz Kwaśnicki, Intrinsic ultracontractivity for stable semigroups on unbounded open sets, Potential Anal. 31(1) (2009): 57–77 [online|MR|zb]
33. Mateusz Kwaśnicki, Spectral gap estimate for stable processes on arbitrary bounded open sets, Probab. Math. Statist. 28(1) (2008): 163–167 [online|MR|zb]
34. Krzysztof Bogdan, Tadeusz Kulczycki, Mateusz Kwaśnicki, Estimates and structure of $\alpha$-harmonic functions, Prob. Theory Rel. Fields 140(3–4) (2008): 345–381 [online|MR|zb]
Note: The first displayed formula in p. 352 should read $w = r^{-2} (r^2 - |x|^2) (r^2 - |v|^2) / |x - v|^2$.

## Papers of my PhD students

• Tomasz Juszczyszyn, Decay rate of harmonic functions fornon-symmetric strictly α-stable Lévy processes, Studia Mathematica 260 (2021): 141–165 [online|MR]
• Jacek Mucha, Spectral theory for one-dimensional (non-symmetric) stable processes killed upon hitting the origin, Electron. J. Probab. 26 (2021), #14: 1–33 [online|MR|zb]

## Selected conference presentations

• Harmonic extensions, operators with completely monotone kernels, and traces of 2-D diffusions [pdf]
Non-local operators, probability and singularities webinar (2020)
• Bell-shaped functions [pdf]
7th Lévy conference (Karlovasi, Greece, 2019)
• Discrete Hilbert transform [pdf]
Gordin Prize lecture (Vilnius, Lithuania, 2018)
• Fractional Laplace operator and operators with unimodal and isotropic kernels [pdf]
Young PDEers at work (Warsaw, Poland, 2018)
• Random walks are completely determined by their trace on the positive half-line [pdf]
Mexico-Poland 1st Meeting in Probability (Guanajuato, Mexico, 2017)
• Fractional Laplace operator in the unit ball [pdf|video]
Stable processes conference (Oaxaca, Mexico, 2016)
• Fractional Laplacian: explicit calculations and applications [pdf]
Nonlocal operators and PDEs (Będlewo, Poland, 2016)
• 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)