Marcin Bownik

Marcin Bownik is a Professor in the Department of Mathematics at the University of Oregon, part of the College of Arts and Sciences. He has been at the University of Oregon since 2003, progressing from Assistant Professor (2003-2008) to Associate Professor (2008-2014) and finally to Professor (2014-present). He has also held visiting positions at the Institute of Mathematics of the Polish Academy of Sciences (2009-2010, 2016-2017, 2023-2024).

Education:

• Ph.D. in Mathematics, Washington University in St. Louis, 2000 (Thesis Advisor: Richard Rochberg)
• M.A. in Mathematics, Washington University in St. Louis, 1997
• Magister in Mathematics, University of Warsaw, Poland, 1995

Marcin Bownik's research focuses on Harmonic Analysis, Wavelets, and Frames. His work spans several interconnected areas including non-isotropic function spaces such as anisotropic Hardy, Besov, and Triebel-Lizorkin spaces; construction of wavelets with arbitrary dilations; theoretical aspects of wavelets and frame wavelets; the structure of shift-invariant spaces in L²(Rⁿ); Gabor systems; and weighted norm inequalities. His recent publications demonstrate continued innovation in anisotropic analysis, frame theory, and applications to operator theory. His work often bridges pure mathematics with applications in signal processing and geometric analysis.

Bownik serves as editor for several prestigious journals including the Journal of Fourier Analysis and Applications (2019-present), Applied and Computational Harmonic Analysis (2020-present), and Dissertationes Mathematicae (2020-present). He has organized numerous conferences and special sessions on Wavelets, Frames, and Related Expansions, demonstrating his leadership in the field.

Ph.D. Students:

• Kenneth Hoover (2007) - Dimension functions of rationally dilated wavelets
• John Jasper (2011) - Infinite dimensional versions of the Schur-Horn theorem
• Li-An Daniel Wang (2012) - Multiplier theorems for anisotropic Hardy spaces
• Joey Iverson (2016) - Frames generated by actions of locally compact groups
• Martin Hiserote (2019) - A characterization of anisotropic H¹(R^N) by smooth homogeneous multipliers

Bownik maintains an active teaching schedule at the University of Oregon, regularly teaching advanced courses in Real Analysis, Complex Analysis, and specialized topics in Harmonic Analysis. His teaching spans from undergraduate calculus courses to graduate-level seminar courses in his research specialty areas.