Friedrich "Fritz" Gesztesy (born 5 November 1953 in Austria) is a well-known Austrian-American mathematical physicist and Professor of Mathematics at Baylor University, known for his important contributions in spectral theory, functional analysis, nonrelativistic quantum mechanics (particularly, Schrödinger operators), ordinary and partial differential operators, and completely integrable systems (soliton equations).

The title of his dissertation 1976 with Heimo Latal and Ludwig Streit was Renormalization, Nelson's symmetry and energy densities in a field theory with quadratic interaction.

[1] After working at the Institut for Theoretical Physics of the University of Graz (1977–82) and several stays abroad at the Bielefeld University (Alexander von Humboldt Scholarship 1980–81 and 1983–84) and at the California Institute of Technology (Max Kade Scholarship 1987–88) he was appointed to Professor at the University of Missouri in 1988 and as Houchins Distinguished Professor in 2002.

In 2016 he joined the faculty of Baylor University as Storm Professor of Mathematics.

[3] Among his students are Gerald Teschl, Karl Unterkofler [1], Selim Sukhtaiev [2], and Maxim Zinchenko [3].