Approximation Theory and Special Functions

This book compiles carefully reviewed papers presented at the international conference "Approximation Theory and Special Functions - ATSF 2024," held in Ankara, Tuerkiye, from September 4-7, 2024. These contributions provide valuable insights into the latest developments at the intersection of approximation theory and special functions. Volume I focuses on topics within approximation theory, including classical approximation by operators, best approximation, operator theory, linear and nonlinear approximation, multivariate approximation, neural networks, numerical approximation, rational approximation, splines, interpolation, and their applications.

With applications spanning mathematics, engineering, economics, and more, approximation theory remains a dynamic research field. This volume covers a wide range of topics, from image processing to financial mathematics, all of which demonstrate the field's relevance. Today, the theory of special functions maintains strong, attractive, and direct connections with various aspects of approximation theory, opening up new avenues for research. This work serves as an invaluable resource for a diverse audience, including researchers, practitioners in approximation theory and special functions, as well as graduate students attending advanced seminars.

ATSF is an international conference series organized to bring together researchers from all areas of Approximation Theory and Special Functions to discuss new ideas and new applications. This organization, which has been held seven times so far as mini-symposia, has grown gradually over the years. The 2024 edition, hosted by TOBB Economics and Technology University in Ankara, marks its eightieth iteration.