This special issue of the Journal of Fourier Analysis and Applications is dedicated to Karlheinz Gröchenig, whose profound and far-reaching contributions have shaped large parts of modern harmonic analysis, in particular time-frequency analysis, Gabor theory, and their numerous applications.Over several decades, his work has provided both deep theoretical insights and powerful methodological tools, influencing a wide spectrum of areas ranging from pure mathematics to signal processing and numerical analysis.Karlheinz Gröchenig's research is characterized by a remarkable synthesis of abstract functional analytic methods with an application oriented perspective.His foundational work on coorbit spaces (with Hans G. Feichtinger) has led to a coherent framework for measuring time-frequency concentration, offering a natural setting for the analysis of pseudodifferential operators and localization phenomena.In parallel, his contributions to Gabor analysis, including the development of localized frames and the systematic study of frame expansions, have become cornerstones of modern time-frequency methods.It builds a bridge between wavelet theory and Gabor analysis and provides a unifying perspective to many other cases where non-orthogonal atomic decompositions, valid for families of Banach spaces, arising from integrable group representations, appear.This principle has inspired many authors since its appearance.
Dahlke et al. (Mon,) studied this question.
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