Projects

• Spezielle Glattheitsmaße und Funktionenräume für Sampling und Interpolation (2025-2027)
  DFG project KO 5804/3-1
  
• Discovering structure in complex data: Statistics meets Optimization and Inverse Problems (2015-2024)
  DFG Research Training Group 2088 (RTG 2088)
  
• Approximation properties of interpolation and quasi-interpolation operators (2018-2021)
  DFG project KO 5804/1

Teaching

• Lecture: An Introduction to Compressed Sensing (English) (WS 2023/2024)
  Monday and Thursday 10.15 - 11.55 (Lecture and Exercises 4 SWS / 6 ECTS)
  
• Lecture: Fourier Analysis and Approximation (English) (SS 2022)
  Tuesday and Friday 8.15 - 09.55 (Lecture+ Exercises: 4 SWS / 6 ECTS)
  

Workshops

• 8th RTG Workshop 2023
  October 4-6, 2023 in Mariaspring, Germany
• From Modeling and Analysis to Approximation and Fast Algorithms (Talk), September 02-06 2023 in Hasenwinkel, Germany
• PhD Retreat 2023 of the RTG 2088 (Talk)
  March 8-10, 2023 in Erfurt, Germany
• 32. Rhein-Ruhr-Workshop (Talk)
  February 10 - February 11, 2023 in Bestwig
• Symposium on Inverse Problems: From experimental data to models and back
  September 19-21, 2022 in Potsdam, Germany
• CRC 1456 Workshop 2022 (Talk)
  August 31 - September 1, 2022 in Goslar, Germany
• 7th RTG Workshop 2022 (Talk)
  August 29-31, 2022 in Goslar, Germany
• Workshop on Data-Driven Methods in Clinical MRI
  June 17 - 18, 2022 in University of Göttingen
• 6th RTG Workshop 2021
  September 6-8, 2021 in Mariaspring, Germany

Publications

• Sharp Lp-error estimates for sampling operators
  Yurii Kolomoitsev, Tetiana Lomako
  J. Approx. Theory, Available online 26 June 2023, 105941, 2023 (preprint available at arXiv)
• Spline Representation and Redundancies of One-Dimensional ReLU Neural Network Models
  Gerlind Plonka, Yannick Nicola Riebe, Yurii Kolomoitsev
  Analysis and Applications 21(01), 127-163, 2023 (preprint available at arXiv)
• On generalized K-functionals in Lp for 0 < p < 1
  Yurii Kolomoitsev, Tetiana Lomako
  Fract. Calc. Appl. Anal. 26, 1016–1030, 2023 (preprint available at arXiv)
• Sparse grid approximation in weighted Wiener spaces
  Yurii Kolomoitsev, Tetiana Lomako, Sergey Tikhonov
  J. Fourier Anal. Appl. 29, 19, 2023 (preprint available at arXiv)
• Uniform approximation by multivariate quasi-projection operators
  Yurii Kolomoitsev, Maria Skopina
  Anal. Math. Phys. 12, no. 2, Paper No. 68, 2022 (preprint available at arXiv)
• Approximation by quasi-interpolation operators and Smolyak's algorithm
  Yurii Kolomoitsev
  J. of Complexity 69, 101601, 2022 (preprint available at arXiv)
• Approximation properties of periodic multivariate quasi-interpolation operators
  Yurii Kolomoitsev, Jürgen Prestin
  J. Approx. Theory 270, 105631, 2021 (preprint available at arXiv)
• Asymptotics of the Lebesgue constants for bivariate approximation processes
  Yurii Kolomoitsev, Tetiana Lomako
  Appl. Math. Comput. 403, 126192, 2021 (preprint available at arXiv)
• Hardy-Littlewood and Ulyanov inequalities
  Yurii Kolomoitsev, Sergey Tikhonov
  Mem. Amer. Math. Soc. 271, no. 1325, 2021 (preprint available at arXiv)
• Asymptotics of the Lebesgue constants for a d-dimensional simplex
  Yurii Kolomoitsev, Elijah Liflyand
  Proc. Amer. Math. Soc. 149, 2911-2926, 2021 (preprint available at arXiv)
• Quasi-projection operators in the weighted Lp spaces
  Yurii Kolomoitsev, Maria Skopina
  Appl. Comput. Harmon. Anal. 52, 165-197, 2021 (preprint available at arXiv)
• Approximation by multivariate quasi-projection operators and Fourier multipliers
  Yurii Kolomoitsev, Maria Skopina
  Appl. Math. Comput. 400, 125955, 2021 (preprint available at arXiv)
• Smoothness of functions vs. smoothness of approximation processes
  Yurii Kolomoitsev, Sergey Tikhonov
  Bull. Math. Sci. 10, no. 3, 2030002, 2020 (preprint available at arXiv)
• Approximation by periodic multivariate quasi-projection operators
  Yurii Kolomoitsev, Aleksandr Krivoshein, Maria Skopina
  J. Math. Anal. Appl. 489, no. 2, 124192, 2020 (preprint available at arXiv)
• Properties of moduli of smoothness in Lp(Rd)
  Yurii Kolomoitsev, Sergey Tikhonov
  J. Approx. Theory 257, 105423, 2020 (preprint available at arXiv)
• Approximation by sampling-type operators in Lp-spaces
  Yurii Kolomoitsev, Maria Skopina
  Math. Methods Appl. Sciences 43, no. 16, 9358-9374, 2020 (preprint available at arXiv)