Book:
K. Bogdan, T. Byczkowski,
T. Kulczycki, M. Ryznar, R. Song, Z. Vondracek, “Potential Analysis of Stable Processes and its
Extensions”, Lecture Notes in Mathematics 1980, Springer,
Papers:
1. S. Jarohs,
T. Kulczycki, P. Salani, “Qualitative properties of
free boundaries for the exterior Bernoulli problem for the half Laplacian”, J.
Math. Anal. Appl. 547 (2025), no. 1, Paper No. 129285, 18 pp.
2. T. Kulczycki, K. Sztonyk,
“Intrinsic ultracontractivity for Schrödinger semigroups based on cylindrical
fractional Laplacian on the plane”, Semigroup Forum 111 (2025), no. 1, 191-226.
3. T. Kulczycki, J. Wszo³a, “On the interior Bernoulli free boundary
problem for the fractional Laplacian on an interval”, Collect. Math. 76 (2025),
no. 1, 11–34.
4. £. Krzywiecki,
T. Kulczycki, C. E. Nteranya, A. Stos,
“Detectable Mislabeling - Can Faulty AI Models be Recognized from Incomplete
Memory Traces?” 2024 IEEE 23rd International Conference on Trust, Security and
Privacy in Computing and Communications (TrustCom), Sanya, China, (2024), pp. 2382-2387.
5. T. Kulczycki, A. Kulik, M. Ryznar, “Drift reduction method for SDEs driven by
inhomogeneous singular Lévy noise”, Bernoulli Vol. 30, Issue 4, (2024),
3089-3118.
6. S. Jarohs,
T. Kulczycki, P. Salani, “On the Bernoulli free
boundary problems for the half Laplacian and for the spectral half Laplacian”,
Nonlinear Anal. 222 (2022), Paper No. 112956, 39 pp.
7. T. Kulczycki, A. Kulik, M. Ryznar, “On weak solution of SDE driven by inhomogeneous
singular Lévy noise”, Trans. Amer. Math. Soc. 375 (2022), 4567-4618.
8. T. Kulczycki, M. Ryznar,
P. Sztonyk, “Strong Feller property for SDEs driven
by multiplicative cylindrical stable noise”, Potential Analysis 55 (2021),
75-126.
9. T. Kulczycki, M. Ryznar,
“Semigroup properties of solutions of SDEs driven by Lévy processes with
independent coordinates”, Stoch. Proc. Appl. 130 (2020) 7185-7217..
10. S. Jarohs,
T. Kulczycki, P. Salani, “Starshape
of the superlevel sets of solutions to equations involving the fractional
Laplacian in starshaped rings”, Mathematische Nachrichten 292 (2019), 1008-1021.
11. T. Kulczycki, M. Ryznar,
“Transition density estimates for diagonal systems of SDEs driven by cylindrical
α-stable processes”, ALEA Lat. Am. J. Probab.
Math. Stat. 15 (2018), 1335-1375.
12. T. Kulczycki, M. Ryznar,
“Gradient estimates of Dirichlet heat kernels for unimodal Lévy processes”, Mathematische Nachrichten 291
(2018), 374-397.
13. T. Kulczycki, “On concavity of
solutions of the Dirichlet problem for the equation (-Δ)1/2 φ
= 1 in convex planar regions”, Journal of the European Mathematical Society 19
(2017), 1361-1420.
14. T. Kulczycki, “Mid-concavity of
survival probability for isotropic Lévy processes”, Electron. Commun. Probab. 21 (2016), no.
29, 1-9.
15. T. Kulczycki, M. Ryznar,
“Gradient estimates of harmonic functions and transition densities for Levy
processes”, Trans. Amer. Math. Soc., 368 (2016), no. 1, 281–318.
16. T. Kulczycki, M. Kwaœnicki,
B. Siudeja, “On the shape of the fundamental sloshing
mode in axisymmetric containers”, Journal of Engineering Mathematics 99 (2016),
157-183.
17. T. Kulczycki, R. Stañczy,
“Multiple solutions for Dirichlet nonlinear BVPs involving fractional
Laplacian”, Discrete Contin. Dyn. Syst. Ser. B 19
(2014), 2581-2591.
18. N.
Kuznetsov, T. Kulczycki, M. Kwaœnicki, A. Nazarov,
S. Poborchi, I. Polterovich,
B. Siudeja, “The legacy of Vladimir Andreevich Steklov”, Notices
Amer. Math. Soc. 61 (2014), 9–22.
19. K. Burdzy,
T. Kulczycki, “Invisibility via
reflecting coating”, J. London Math. Soc. 88 (2013), 359-374.
20. T. Kulczycki, “Gradient estimates of q-harmonic functions
of fractional Schrödinger operator”,
Potential Analysis 39 (2013), 69–98.
21. K.
Burdzy, T. Kulczycki, R. Schilling, ”Stationary distributions for jump processes
with inert drift”, in “Malliavin Calculus and Stochastic Analysis: A Festschrift
in Honor of David Nualart”, Springer Proceedings in
Mathematics & Statistics 34, Springer Science+Business
Media New York (2013), 139-172.
22. T.
Kulczycki, M. Kwaœnicki, ”On high spots of the fundamental sloshing
eigenfunctions in axially symmetric domains”,
Proc. London Math. Soc. 105 (2012),
921-952.
23. K. Burdzy, T. Kulczycki, R. Schilling, "Stationary
distributions for jump processes with memory" Ann. Inst. Henri Poincaré Probab. Stat. 48 (2012), 609–630.
24. T. Kulczycki, N.
Kuznetsov, “On the ‘high spots’ of fundamental sloshing modes in a trough”,
Proc. Roy. Soc. London Ser. A 467
(2011), 1491-1502.
25. R.
Bañuelos, T. Kulczycki, I. Polterovich,
B. Siudeja, “Eigenvalue inequalities for mixed Steklov problems”,
Operator Theory and Its Applications: In Memory of V. B. Lidskii (1924-2008), Advances in the Mathematical Sciences,
AMS Translations 231, (2010), pp. 19-34.
26. K. Kaleta, T. Kulczycki, ”Intrinsic ultracontractivity for
Schrödinger operators based on fractional Laplacians”, Potential Analysis 33
(2010), 313-339 .
27. T.
Kulczycki, M. Kwaœnicki, J. Ma³ecki,
A. Stós, ”Spectral properties of the Cauchy process
on half-line and interval”, Proc. London. Math. Soc. 101 (2010), 589-622.
28. R. Bañuelos, T. Kulczycki, B. Siudeja,
“On the trace of symmetric stable processes on Lipschitz domains”, J. Funct. Anal. 257 (2009), no. 10, 3329-3352.
29. T. Kulczycki, N. Kuznetsov, “’High spots' theorems for sloshing problems”,
Bull. Lond. Math. Soc. 41 (2009), 495-505.
30. R. Bañuelos,
T. Kulczycki, B. Siudeja, “Neumann Bessel Heat Kernel
Monotonicity”, Potential Anal. 30 (2009), no. 1, 65-83.
31. R. Bañuelos,
T. Kulczycki, “Trace estimates for stable processes”, Probab.
Theory Relat. Fields 142 (2008), 313-338.
32. K. Bogdan, T. Kulczycki,
M. Kwaœnicki, “Estimates and structure of
α-harmonic functions”, Probab. Theory Relat. Fields140 (2008), 345-381.
33. B. Dyda,
T. Kulczycki, “Spectral gap for stable process on convex double symmetric
domains”, Potential Anal. 27 (2007), 101-132.
34. R. Bañuelos,
T. Kulczycki, „Spectral gap for the Cauchy process on convex, symmetric
domains”, Comm. Partial Differential Equations 31 (2006), 1841–1878.
35. R. Bañuelos,
T. Kulczycki, P. Mendez-Hernandez, „On the shape of the ground state
eigenfunction for stable processes”, Potential Anal. 24 (2006), 205-221.
36. R. Bañuelos,
T. Kulczycki, „Eigenvalue gaps for the Cauchy process and a Poincare
inequality”, J. Funct. Anal 234 (2006), 199-225.
37. T. Kulczycki, B. Siudeja, „Intrinsic ultracontractivity of Feynman-Kac
semigroup for relativistic stable processes”, Trans. Amer. Math. Soc.
358(11) (2006), 5025--5057.
38. R. Bañuelos,
T. Kulczycki, “The Cauchy process and the Steklov
problem” J. Funct. Anal. 211 (2004), no. 2, 355--423.
39. K. Burdzy,
T. Kulczycki, “Stable processes have thorns” Ann. Probab.
31 (2003), no. 1, 170--194.
40. K. Bogdan, T. Kulczycki,
A. Nowak, “Gradient estimates for harmonic and $q$-harmonic functions of
symmetric stable processes” Illinois J. Math. 46 (2002), no. 2, 541--556.
41. T. Kulczycki, “Exit time
and Green function of cone for symmetric stable processes” Probab.
Math. Statist. 19 (1999), no. 2, 337--374.
42. T. Kulczycki, “Intrinsic
ultracontractivity for symmetric stable processes” Bull. Polish Acad. Sci.
Math. 46 (1998), no. 3, 325--334.
43. T. Kulczycki “Properties
of Green function of symmetric stable processes” Probab.
Math. Statist. 17 (1997), no. 2, 339--364.