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. K. Burdzy,
T. Kulczycki, “Invisibility
via reflecting coating”, Journal London Math. Soc. (to appear).
2. T. Kulczycki, “Gradient estimates of q-harmonic functions
of fractional Schrödinger operator”,
Potential Analysis, published online November 9, 2012, doi:10.1007/s11118-012-9322-9.
3. T. Kulczycki, M. Kwaœnicki, ”On high spots of the fundamental sloshing eigenfunctions in axially symmetric domains”, Proc. London Math. Soc. 105 (2012), 921-952.
4. K. Burdzy, T. Kulczycki, R.
Schilling, ”Stationary distributions for
jump processes with inert drift”,
Festschrift in Honor of David Nualart,
Proceedings in Mathematics Series, Springer.
(to appear).
5. K. Burdzy, T. Kulczycki, R.
Schilling, "Stationary distributions for jump processes with memory"
Ann. Inst. Henri Poincaré Probab.
Stat. 48 (2012), 609–630.
6. 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.
7. 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.
8. K. Kaleta, T. Kulczycki, ”Intrinsic ultracontractivity for Schrödinger operators based on
fractional Laplacians”, Potential Analysis 33 (2010),
313-339 .
9. 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.
10. 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.
11. T. Kulczycki,
N. Kuznetsov, “’High spots' theorems for sloshing
problems”, Bull. Lond. Math. Soc. 41 (2009), 495-505.
12. R. Bañuelos,
T. Kulczycki, B. Siudeja,
“Neumann Bessel Heat Kernel Monotonicity”, Potential Anal. 30 (2009), no. 1,
65-83.
13. R. Bañuelos,
T. Kulczycki, “Trace estimates for stable
processes”, Probab. Theory Relat.
Fields 142 (2008), 313-338.
14. K. Bogdan,
T. Kulczycki, M. Kwaœnicki,
“Estimates and structure of α-harmonic functions”, Probab. Theory Relat. Fields140
(2008), 345-381.
15. B. Dyda,
T. Kulczycki, “Spectral gap for stable process on
convex double symmetric domains”, Potential Anal. 27 (2007), 101-132.
16. R. Bañuelos,
T. Kulczycki, „Spectral gap for the Cauchy
process on convex, symmetric domains”, Comm. Partial Differential
Equations 31 (2006), 1841–1878.
17. R. Bañuelos,
T. Kulczycki, P. Mendez-Hernandez, „On the
shape of the ground state eigenfunction for stable
processes”, Potential Anal. 24 (2006), 205-221.
18. R. Bañuelos,
T. Kulczycki, „Eigenvalue gaps for the Cauchy
process and a Poincare inequality”, J. Funct. Anal
234 (2006), 199-225.
19. T. Kulczycki,
B. Siudeja, „Intrinsic ultracontractivity
of Feynman-Kac semigroup
for relativistic stable processes”, Trans. Amer. Math. Soc. 358(11)
(2006), 5025--5057.
20. R. Bañuelos,
T. Kulczycki, “The Cauchy process and the Steklov problem” J. Funct. Anal.
211 (2004), no. 2, 355--423.
21. K. Burdzy,
T. Kulczycki, “Stable processes have thorns” Ann. Probab. 31 (2003), no. 1, 170--194.
22. 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.
23. T. Kulczycki,
“Exit time and Green function of cone for symmetric stable processes” Probab. Math. Statist. 19 (1999), no. 2, 337--374.
24. T. Kulczycki,
“Intrinsic ultracontractivity for symmetric stable
processes” Bull. Polish Acad. Sci. Math. 46 (1998), no. 3, 325--334.
25. T. Kulczycki
“Properties of Green function of symmetric stable processes” Probab. Math. Statist. 17 (1997), no. 2, 339--364.