Hans Georg Feichtinger earned his doctoral degree in 1974 from the University of Vienna, where he remains a faculty member today. Born in Wiener Neustadt in 1951, he has spent decades advancing the fields of harmonic analysis, time-frequency theory, and irregular sampling, establishing himself as a foundational figure in contemporary mathematical research and education.
Academic Foundation
Feichtinger completed his secondary education at the Gymnasium in Wiener Neustadt, graduating with the Matura summa cum laude in 1969. He subsequently enrolled at the University of Vienna to study physics and mathematics. His doctoral studies, supervised by Hans Reiter, culminated in a 1974 thesis focused on subalgebras of L1(G). By 1979, he achieved his habilitation with a thesis regarding Banach convolution algebras of functions.
Numerical Harmonic Analysis Group
In the late 1980s, Feichtinger began collaborating with Karlheinz Gröchenig on atomic decompositions. Following subsequent research on irregular sampling with Thomas Strohmer, he founded the Numerical Harmonic Analysis Group at the University of Vienna. The group, which traces its roots to projects started in 1986, evolved into an international hub for abstract and applied harmonic analysis, hosting approximately 40 researchers.
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His primary research interests include Gabor analysis, frame theory, and function spaces. In the early 1980s, he introduced modulation spaces, which are now standard tools in time-frequency analysis based on the short-time Fourier transform. He also developed Wiener amalgam spaces in 1980 to treat local and global behaviors of functions separately. Furthermore, his collaborative work with Gröchenig produced coorbit theory, providing a unified framework for wavelet and short-time Fourier transforms.
Feichtinger's Conjecture
During his career, he posed a question regarding whether every bounded frame could be expressed as a finite union of Riesz basic sequences. This proposition, identified as Feichtinger's conjecture by Peter G. Casazza, represents a critical problem in frame theory. It was eventually determined to be equivalent to the Kadison–Singer problem. A complete proof for the conjecture was provided by Adam Marcus, Daniel A. Spielman, and Nikhil Srivastava in 2013.
Editorial and Pedagogical Service
Feichtinger has maintained a long tenure as the editor-in-chief of the Journal of Fourier Analysis and Applications, a role he assumed in 2000. He serves as an associate editor for several publications, including the Journal of Approximation Theory. Beyond research, he has supervised 23 completed PhD theses and acted as a contact for the European Union's LEONARDO student exchange program at the University of Vienna.
Fast facts
- Born: 1951, Wiener Neustadt, Austria
- PhD: University of Vienna, 1974
- Primary research field: Harmonic analysis
- Notable contribution: Modulation spaces
- Group founded: Numerical Harmonic Analysis Group
- Publications: Approximately 200 scientific articles
- Academic role: Professor at the University of Vienna
- Doctoral supervisor: Hans Reiter
Questions readers ask
What is Feichtinger's conjecture?
It is a mathematical proposition questioning whether every bounded frame can be written as a finite union of Riesz basic sequences, later proven equivalent to the Kadison–Singer problem.
What is the NuHAG?
The Numerical Harmonic Analysis Group is a research group based at the University of Vienna, founded by Feichtinger, focused on abstract and applied harmonic analysis.
Achievements
- Held posts at University of Vienna and Technical University of Denmark
- Fields: mathematician
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