Bartosz Trojan

Research interests

In preparation

• with G. Świderski, Spectral properties of some Sturm--Liouville operators
• with T. Grzywny, Z. Palmowski, K. Szczypkowski, Stationary states for stable processes with partial resetting

Preprints

37. with G. Świderski Asymptotic distribution of zeros of orthogonal polynomials with unbounded recurrence coefficients, submited, arXiv: pdf
38. with J.-Ph. Anker, Optimal bounds for the Dunkl kernel in the dihedral case, submited, arXiv: pdf
39. with J.-Ph. Anker, B. Rémy, Construction of Brooks-Lindenstrauss kernels on affine buildings of arbitrary reduced type, with applications, preprint
40. with T. Grzywny, Subordinated Markov processes: sharp estimates for heat kernels and the Green functions submited, arXiv: pdf
41. with B. Rémy, Martin compactifications of affine buildings, submited, arXiv: pdf
42. Asymptotic behaviour of heat kernels and Green functions on affine buildings, submited, arXiv: pdf
43. with J-Ph. Anker, and B. Schapira, Sharp estimates for a distinguished random walk\\on affine buildings of type \(\tilde{A}_r\), submited, arXiv: pdf

Papers

30. with G. Świderski, Orthogonal polynomials with periodically modulated recurrence coefficients in the Jordan block case II Constructive Approximation, 58 (2023), 615-686, arXiv: pdf
29. with G. Świderski, Orthogonal polynomials with periodically modulated recurrence coefficients in the Jordan block case, accepted to Annales l'Institut Fourier, arXiv: pdf
30. with M. Rzeszut, A biparameter decemposition of Davis-Garsia type, Studia Mathematics, 269 (2023), 167-191, local: pdf
31. with G. Świderski, About essential spectra of unbounded Jacobi matrices, Journal of Approximation Theory, 278 (2022), 105746, arXiv: pdf
32. with T. Grzywny and Ł. Leżaj, Transition densities of subordinators of positive order, Journal of the Institute of Mathematics of Jussieu, (2021), 1119-1179, arXiv: pdf
33. Weak type \( (1, 1) \) estimates for maximal functions along \(1\)-regular sequences of integers, Studia Mathematica, 261 (2021), 103-108, arXiv: pdf
34. with G. Świderski, Asymptotic behaviour of Christoffel–Darboux kernel via three-term recurrence relation II, Journal of Approximation Theory, 261 (2020), 105496, arXiv: pdf
35. with G. Świderski, Asymptotic behaviour of Christoffel–Darboux kernel via three-term recurrence relation I, Constructive Approximation, 54 (2020), 49-116, arXiv: pdf
36. with G. Świderski, Asymptotics of orthogonal polynomials with slowly oscillating recurrence coefficients, Journal of Functional Analysis 278 (2020), 108326, arXiv: pdf
37. Endpoint estimates for the maximal function over prime numbers, Journal of Fourier Analysis And Applications 25 (2019), 3123-3153, arXiv: pdf
38. Long time behaviour of random walks on the integer lattice, Monatshefte für Mathematik 191 (2020), arXiv: pdf
39. Variational estimates for operators on some thin subsets of primes, Mathematical Research Letters 27 (2020), arXiv: pdf
40. Variational estimates for discrete operators modeled on multi-dimensional polynomial subsets of primes, Mathematische Annalen 374 (2019), 1597-1656, arXiv: pdf
41. 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
42. with T. Steger, Littlewood-Paley theory for tringle buildings, Journal of Geometric Analysis 28 (2018), 1122-1150, arXiv: pdf
43. with B. Krause, and M. Mirek, Two-parameter version of Bourgain's inequality: Rational frequencies, Advances in Mathematics 323 (2018), 720-744, arXiv: pdf
44. 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
45. with G. Świderski, Periodic perturbations of unbounded Jacobi matrices I: Asymptotics of generalized eigenvectors, Journal of Approximation Theory 216 (2017), 38-66, arXiv: pdf
46. 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
47. 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
48. 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
49. with A. Bendikov, and W. Cygan, Limit theorems for random walks, Stochastic Processes and their Applications 127 (2017), 3268-3290, arXiv: pdf
50. with M. Mirek, Discrete maximal functions in higher dimensions and applications to ergodic theory, American Journal of Mathematics 138 (2016), 1495-1532, arXiv: pdf
51. 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
52. 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
53. with M. Mirek, Cotlar's ergodic theorem along the prime numbers, Journal of Fourier Analysis And Applications 21 (2015), 822-848, arXiv: pdf
54. 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,
55. Asymptotic Expansions and Hua-harmonic functions on bounded homogeneous domains, Mathematische Annalen 336 (2006), 73-110,
56. 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
57. Poisson kernel and pluriharmonic \(\mathcal{H}^2\) functions on homogeneous Siegel domains, Journal of Lie Theory 12 (2002), 217-243,