Special measures of smoothness and function spaces for sampling and interpolation

• Applicant: Dr. Yurii Kolomoitsev
• Subject Area: Mathematics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 562347022

The research project focuses on the study of various problems in the approximation of functions by sampling and interpolation operators for broad classes of functions in Lp spaces and more general Banach and quasi-Banach spaces. In particular, we plan to consider function classes that include highly oscillatory functions, singular functions, fractal functions, functions with unbounded values, and others. The main goal is to develop new special measures of smoothness and function spaces based on the concept of averaged local smoothness, and to apply them in the analysis of the approximation properties of sampling and interpolation processes. The outcomes aim to provide novel and effective methods and tools for addressing non-standard classes of functions within the frameworks of sampling and interpolation theory.

• DFG Programme: Research Grants