Bartosz Trojan

Research interests

In preparation

• with J.-Ph. Anker, C. Peterson, B. Rémy, Multi-temporal wave equations on affine buildings
• with T. Grzywny, Z. Palmowski, K. Szczypkowski, Kernels and densities with random resetting
• with T. Grzywny, E. Papageorgiou, Caloric functions on measure metric spaces
• with E. Papageorgiou, Herz majorization on affine buildings
• with S. Kupin, G. Świderski, Orthogonal polynomials with irregular Jacobi parameters
• with S. Kupin, G. Świderski, Uniform bounds for orthogonal polynomials
• with A. Nevo, B. Rémy, Weak type \((1, 1)\) estimates for maximal functions on affine buildings

Preprints

41. with T. Grzywny, Subordinated semigroups: sharp estimates for heat kernels and the Green functions, submited, arXiv: pdf

Papers

40. with J.-Ph. Anker, B. Rémy, Construction of Brooks-Lindenstrauss kernels on affine buildings of arbitrary reduced type, with applications, Mathematische Annalen (2026), arXiv: pdf
39. with E. Papageorgiou, Mass Functions and Asymptotic Behavior of Caloric Functions on Affine Buildings, Mathematische Annalen 395 (2026), 30, arXiv: pdf
38. with G. Świderski, Sturm--Liouville operators with periodically modulated parameters. Part I: Regular case , Journal of Differential Equations 464 (2026), 114188, arXiv: pdf
37. with B. Rémy, Martin compactifications of affine buildings, Journal of the European Mathematical Society 28 (2026), 1979-2066, arXiv: pdf
36. with T. Grzywny, Z. Palmowski, K. Szczypkowski, Stationary states for stable processes with partial resetting, Annals of Applied Probability 36 (2026), 1110-1177, arXiv: pdf
35. with G. Świderski, Asymptotic distribution of zeros of orthogonal polynomials with unbounded recurrence coefficients, Journal of Functional Analysis 289 (2025), 111162, arXiv: pdf
34. with C. Di Bello, A. Chechkin, T. Grzywny, K. Szczypkowski, Z. Palmowski, Partial versus total resetting for Lévy flights in d dimensions: similarities and discrepancies, Chaos 35 (2025), 043129
33. with J.-Ph. Anker, Optimal bounds for the Dunkl kernel in the dihedral case, Journal of Functional Analysis 288 (2025), 110743, arXiv: pdf
32. Asymptotic behaviour of heat kernels and Green functions on affine buildings, Journal of the European Mathematical Society 27 (2025), 4649-4703, arXiv: pdf
33. with J-Ph. Anker, and B. Schapira, Sharp estimates for a distinguished random walk on affine buildings of type \(\tilde{A}_r\), Indagationes Mathematicae 36 (2025), 383-412, arXiv: pdf
34. with G. Świderski, Orthogonal polynomials with periodically modulated recurrence coefficients in the Jordan block case, Annales l'Institut Fourier 74 (2024), 1521-1601, arXiv: pdf
35. with G. Świderski, Orthogonal polynomials with periodically modulated recurrence coefficients in the Jordan block case II, Constructive Approximation 58 (2023), 615-686, arXiv: pdf
36. with M. Rzeszut, A biparameter decemposition of Davis-Garsia type, Studia Mathematics 269 (2023), 167-191, local: pdf
37. with T. Grzywny and Ł. Leżaj, Transition densities of subordinators of positive order, Journal of the Institute of Mathematics of Jussieu 22 (2023), 1119-1179, arXiv: pdf
38. with G. Świderski, About essential spectra of unbounded Jacobi matrices, Journal of Approximation Theory 278 (2022), 105746, arXiv: pdf
39. Weak type \( (1, 1) \) estimates for maximal functions along \(1\)-regular sequences of integers, Studia Mathematica 261 (2021), 103-108, arXiv: pdf
40. with G. Świderski, Asymptotic behaviour of Christoffel–Darboux kernel via three-term recurrence relation II, Journal of Approximation Theory 261 (2020), 105496, arXiv: pdf
41. with G. Świderski, Asymptotic behaviour of Christoffel–Darboux kernel via three-term recurrence relation I, Constructive Approximation 54 (2020), 49-116, arXiv: pdf
42. with G. Świderski, Asymptotics of orthogonal polynomials with slowly oscillating recurrence coefficients, Journal of Functional Analysis 278 (2020), 108326, arXiv: pdf
43. Endpoint estimates for the maximal function over prime numbers, Journal of Fourier Analysis And Applications 25 (2019), 3123-3153, arXiv: pdf
44. Long time behaviour of random walks on the integer lattice, Monatshefte für Mathematik 191 (2020), arXiv: pdf
45. Variational estimates for operators on some thin subsets of primes, Mathematical Research Letters 27 (2020), arXiv: pdf
46. Variational estimates for discrete operators modeled on multi-dimensional polynomial subsets of primes, Mathematische Annalen 374 (2019), 1597-1656, arXiv: pdf
47. with M. Mirek, and E.M. Stein, \(\ell^p(\mathbb{Z}^d)\)-estimates for discrete operators of Radon type: Maximal functions and vector-valued estimates, Journal of Functional Analysis 277 (2019), 2471-2521, arXiv: pdf
48. with T. Steger, Littlewood-Paley theory for tringle buildings, Journal of Geometric Analysis 28 (2018), 1122-1150, arXiv: pdf
49. with B. Krause, and M. Mirek, Two-parameter version of Bourgain's inequality: Rational frequencies, Advances in Mathematics 323 (2018), 720-744, arXiv: pdf
50. with G. Grzywny, and M. Ryznar, Asymptotic behaviour and estimates of slowly varying convolution semigroups, International Mathematics Research Notices 23 (2019), 7193-7258 arXiv: pdf
51. with G. Świderski, Periodic perturbations of unbounded Jacobi matrices I: Asymptotics of generalized eigenvectors, Journal of Approximation Theory 216 (2017), 38-66, arXiv: pdf
52. with M. Mirek, and P. Zorin-Kranich, Variational estimates for averages and truncated singular integrals along the prime numbers, Transactions of the American Mathematical Society 369 (2017), 5403-5423, arXiv: pdf
53. with M. Mirek, and E.M. Stein, \(\ell^p\big(\mathbb{Z}^d\big)\)-estimates for discrete operators of Radon types: Variational estimates, Inventiones Mathematicae 209 (2017), 665-748, arXiv: pdf
54. with W. Cygan, and T. Grzywny, Asymptotic behaviour of densities of unimodal convolution semigroups, Transactions of the American Mathematical Society 369 (2017), 5623-5644, arXiv: pdf
55. with A. Bendikov, and W. Cygan, Limit theorems for random walks, Stochastic Processes and their Applications 127 (2017), 3268-3290, arXiv: pdf
56. with M. Mirek, Discrete maximal functions in higher dimensions and applications to ergodic theory, American Journal of Mathematics 138 (2016), 1495-1532, arXiv: pdf
57. with B. Krause, and M. Mirek On the Hardy-Littlewood majorant problem for arithmetic sets, Journal of Functional Analysis 271 (2016), 164-181, arXiv: pdf
58. with K. Hughes, and B. Krause The maximal function and conditional square function control the variation: An elementary proof, Proceedings of The American Mathematical Society 144 (2016), 3583-3588, arXiv: pdf
59. with M. Mirek, Cotlar's ergodic theorem along the prime numbers, Journal of Fourier Analysis And Applications 21 (2015), 822-848, arXiv: pdf
60. with C. Nana, \(L^p\) boundedness of Bergman projections in tube domains over homogeneous cones, Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze 5 (2011), 477-511,
61. Asymptotic Expansions and Hua-harmonic functions on bounded homogeneous domains, Mathematische Annalen 336 (2006), 73-110,
62. with A. Bonami, D. Buraczewski, E. Damek, A. Hulanicki, and R. Penney, Hua-harmonic functions on symmetric irreducible Siegel domains of type II, Journal of Functional Analysis 188 (2002), 38-74, arXiv: pdf
63. Poisson kernel and pluriharmonic \(\mathcal{H}^2\) functions on homogeneous Siegel domains, Journal of Lie Theory 12 (2002), 217-243,