Projects funded by the NCN

Information on the principal investigator and host institution

Information of the project and the call

Keywords

Equipment

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Spherical analysis, maximal operators and orthogonal expansions

2017/27/B/ST1/01623

Keywords:

spherical heat kernel sharp estimate spherical Brownian motion spherical Radon transform spherical means discrete spherical means maximal operator Fourier-Bessel expansions Sobolev spaces Riesz transforms conjugacy potential operator Hankel transform Bessel operator Laguerre expansions Laguerre operator Jacobi expansions Jacobi operator Dunkl transform Dunkl Laplacian generalized Hermite functions Dunkl harmonic oscillator generalized Hermite polynomials Dunkl Ornstein-Uhlenbeck operator

Descriptors:

  • ST1_8: Analysis

Panel:

ST1 - Mathematics: all areas of mathematics, pure and applied, as well as mathematical foundations of computer science, physics and statistics

Host institution :

Instytut Matematyczny Polskiej Akademii Nauk

woj. mazowieckie

Other projects carried out by the institution 

Principal investigator (from the host institution):

prof. Adam Nowak 

Number of co-investigators in the project: 3

Call: OPUS 14 - announced on 2017-09-15

Amount awarded: 599 000 PLN

Project start date (Y-m-d): 2018-06-29

Project end date (Y-m-d): 2022-12-28

Project duration:: 54 months (the same as in the proposal)

Project status: Project settled

Project description

Download the project description in a pdf file

Note - project descriptions were prepared by the authors of the applications themselves and placed in the system in an unchanged form.

Equipment purchased [PL]

  1. Monitor o wysokiej rozdzielczości i dużym rozmiarze.
  2. Akcesoria do aparatury: stacja dokująca do laptopa i ramię obrotowe/wysięgnik do monitora.
  3. Kamera internetowa/wizualizer na statywie o wysokiej rozdzielczości.
  4. laptop/notebook (3 szt.) (19 500 PLN)
  5. Oprogramowanie do obliczeń symbolicznych/numerycznych: MAPLE (5 500 PLN)

Information in the final report

  • Publication in academic press/journals (17)
  1. Dimension-free estimates for the discrete spherical maximal functions
    Authors:
    Mariusz Mirek, Tomasz Zachary Szarek, Błażej Wróbel
    Academic press:
    International Mathematics Research Notices (rok: 2023, tom: jeszcze nie wiadomo, strony: 63 pp.), Wydawca: Oxford University Press
    Status:
    Published
    DOI:
    10.1093/imrn/rnac329 - link to the publication
  2. Genuinely sharp heat kernel estimates on compact rank-one symmetric spaces, for Jacobi expansions, on a ball and on a simplex
    Authors:
    Adam Nowak, Peter Sjögren, Tomasz Zachary Szarek
    Academic press:
    Mathematische Annalen (rok: 2021, tom: 381, strony: 1455-1476), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00208-021-02185-8 - link to the publication
  3. Lattice points problem, equidistribution and ergodic theorems for certain arithmetic spheres
    Authors:
    Alex Iosevich, Bartosz Langowski, Mariusz Mirek, Tomasz Zachary Szarek
    Academic press:
    Mathematische Annalen (rok: 2023, tom: jeszcze nie wiadomo, strony: 80 pp.), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00208-022-02557-8 - link to the publication
  4. On non-centered maximal operators related to a non-doubling and non-radial exponential measure
    Authors:
    Adam Nowak, Emanuela Sasso, Peter Sjögren, Krzysztof Stempak
    Academic press:
    Mathematische Annalen (rok: 2023, tom: jeszcze nie wiadomo, strony: 43 pp.), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00208-023-02595-w - link to the publication
  5. Maximal estimates for a generalized spherical mean Radon transform acting on radial functions
    Authors:
    Óscar Ciaurri, Adam Nowak, Luz Roncal
    Academic press:
    Annali di Matematica Pura ed Applicata (rok: 2020, tom: 199, strony: 1597-1619), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s10231-019-00933-x - link to the publication
  6. Oscillation inequalities in ergodic theory and analysis: one-parameter and multi-parameter perspectives
    Authors:
    Mariusz Mirek, Tomasz Zachary Szarek, James Wright
    Academic press:
    Revista Matemática Iberoamericana (rok: 2022, tom: 38, strony: 2249-2284), Wydawca: EMS Press
    Status:
    Published
    DOI:
    10.4171/RMI/1383 - link to the publication
  7. Restriction of exponential sums to hypersurfaces
    Authors:
    Ciprian Demeter, Bartosz Langowski
    Academic press:
    International Mathematics Research Notices (rok: 2023, tom: 2023, strony: 1292-1354), Wydawca: Oxford University Press
    Status:
    Published
    DOI:
    10.1093/imrn/rnab278 - link to the publication
  8. Sharp lp-improving estimates for the discrete paraboloid
    Authors:
    Shival Dasu, Ciprian Demeter, Bartosz Langowski
    Academic press:
    Journal of Fourier Analysis and Applications (rok: 2021, tom: 27, strony: 45310), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00041-020-09801-2 - link to the publication
  9. Exotic multiplicity functions and heat maximal operators in certain Dunkl settings
    Authors:
    Alberto Arenas, Edgar Labarga, Adam Nowak
    Academic press:
    Integral transforms and special functions (rok: 2018, tom: 29, strony: 771-793), Wydawca: Taylor & Francis
    Status:
    Published
    DOI:
    10.1080/10652469.2018.1498488 - link to the publication
  10. Oscillation inequalities for Radon averages
    Authors:
    Bartosz Langowski
    Academic press:
    AMS Contemporary Mathematics Series (rok: 2023, tom: jeszcze nie wiadomo, strony: 11 pp.), Wydawca: American Mathematical Society
    Status:
    Submitted
    DOI:
    brak - link to the publication
  11. Mapping properties of fundamental harmonic analysis operators in the exotic Bessel framework
    Authors:
    Bartosz Langowski, Adam Nowak
    Academic press:
    Journal of Mathematical Analysis and Applications (rok: 2021, tom: 499, strony: 1-36, article id 125061), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jmaa.2021.125061 - link to the publication
  12. Some remarks on oscillation inequalities
    Authors:
    Mariusz Mirek, Wojciech Słomian, Tomasz Zachary Szarek
    Academic press:
    Ergodic Theory and Dynamical Systems (rok: 2022, tom: jeszcze nie wiadomo, strony: 30 pp.), Wydawca: Cambridge University Press
    Status:
    Published
    DOI:
    10.1017/etds.2022.77 - link to the publication
  13. Endpoint estimates and optimality for the generalized spherical maximal operator on radial functions
    Authors:
    Adam Nowak, Luz Roncal, Tomasz Zachary Szarek
    Academic press:
    Communications on Pure and Applied Analysis (rok: 2023, tom: jeszcze nie wiadomo, strony: 45 pp.), Wydawca: American Institute of Mathematical Sciences
    Status:
    Accepted for publication
    DOI:
    brak - link to the publication
  14. Polynomial sequences in discrete nilpotent groups of step 2
    Authors:
    Alexandru Ionescu, Ákos Magyar, Mariusz Mirek, Tomasz Zachary Szarek
    Academic press:
    Advanced Nonlinear Studies (rok: 2023, tom: jeszcze nie wiadomo, strony: 25 pp.), Wydawca: De Gruyter
    Status:
    Submitted
    DOI:
    brak - link to the publication
  15. On derivatives, Riesz transforms and Sobolev spaces for Fourier-Bessel expansions
    Authors:
    Bartosz Langowski, Adam Nowak
    Academic press:
    Journal of Fourier Analysis and Applications (rok: 2022, tom: 28, strony: 21551), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00041-021-09896-1 - link to the publication
  16. Polynomial averages and pointwise ergodic theorems on nilpotent groups
    Authors:
    Alexandru Ionescu, Ákos Magyar, Mariusz Mirek, Tomasz Zachary Szarek
    Academic press:
    Inventiones Mathematicae (rok: 2022, tom: jeszcze nie wiadomo, strony: 118 pp.), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00222-022-01159-0 - link to the publication
  17. Sharp estimates of the spherical heat kernel
    Authors:
    Adam Nowak, Peter Sjögren, Tomasz Zachary Szarek
    Academic press:
    Journal de Mathématiques Pures et Appliquées (rok: 2019, tom: 129, strony: 23-33), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.002 - link to the publication

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