Fritz Gesztesy, Ph.D.
Ralph and Jean Storm Professor of Mathematics
Education
Ph.D., University of Graz, Austria, 1976.
Biography
Dr. Gesztesy joined the Baylor faculty as Storm Professor of Mathematics in August of 2016. Prior to Baylor he taught for 28 years at the University of Missouri, Columbia (1988-2016) and for 11 years at the University of Graz, Austria (1977-1988). He was Assistant Professor (Jan. 1977 - May 1982) and Associate Professor (June 1982 - Aug. 1988) at the Institute for Theoretical Physics of the University of Graz, Austria, Professor of Mathematics at the University of Missouri, Columbia (Sept. 1988 - Aug. 2016), and Houchins Distinguished Professor (Jan. 2002 - Aug. 2016) at the latter institution. He has lectured and held visiting positions at numerous institutions and supervised 7 Masters and 14 Ph.D. students. Currently, he is Editor in Chief of the Journal of Spectral Theory (EMS).
Academic Interests and Research
Dr. Gesztesy’s research centers around applications of operator and spectral theory to a variety of problems connected to mathematical physics. More specifically, his areas of interest include Mathematical Physics, Spectral Theory, Operator Theory, Differential Equations, Completely Integrable Systems.
Selected Publications
Limits of soliton solutions; with W. Karwowski and Z. Zhao, Duke Math. J. 68, 101-150 (1992).
The xi function; with B. Simon, Acta Math. 176, 49-71 (1996).
Picard potentials and Hill's equation on a torus; with R. Weikard, Acta Math. 176, 73-107 (1996).
A characterization of all elliptic solutions of the AKNS hierarchy; with R. Weikard, Acta Math. 181, 63-108 (1998).
A new approach to inverse spectral theory, II. General real potentials and the connection to the spectral measure; with B. Simon, Ann. of Math. 152, 593-643 (2000).
Variations on a theme of Jost and Pais; with M. Mitrea and M. Zinchenko, J. Funct. Anal. 253, 399-448 (2007).
Real-valued algebro-geometric solutions of the Camassa-Holm hierarchy; with H. Holden, Phil. Trans. Roy. Soc. London Ser. A 366, 1025-1054 (2008).
Local spectral properties of reflectionless Jacobi, CMV, and Schrödinger operators; with M. Zinchenko, J. Diff. Eq. 246, 78-107 (2009).
Spectral theory for perturbed Krein Laplacians in nonsmooth domains; with M. Ashbaugh, M. Mitrea, and G. Teschl, Adv. Math. 223, 1372-1467 (2010).
The index formula and the spectral shift function for relatively trace class perturbations; with Y. Latushkin, K.A. Makarov, F. Sukochev, and Y. Tomilov, Adv. Math. 227, 319-420 (2011).
A Schauder and Riesz basis criterion for non-self-adjoint Schrödinger operators with periodic and antiperiodic boundary conditions; with V. Tkachenko, J. Diff. Eq. 253, 400-437 (2012).
Heat kernel bounds for elliptic partial differential operators in divergence form with Robin-type boundary conditions; with M. Mitrea and R. Nichols, J. Analyse Math. 122, 229-287 (2014).
The Callias index formula revisited; with M. Waurick, Springer Lecture Notes in Math., Vol. 2157 (2016).
Decoupling of deficiency indices and applications to Schrödinger-type operators with possibly strongly singular potentials; with M. Mitrea, I. Nenciu, and G. Teschl, Adv. Math. 301, 1022-1061 (2016).
Spectral shift functions and Dirichlet-to-Neumann maps; with J. Behrndt and S. Nakamura, Math. Ann. 371, 1255-1300 (2018).
Books
Solvable Models in Quantum Mechanics, 2nd edition; with S. Albeverio, R. Høegh-Krohn, and H. Holden, AMS-Chelsea Series, Amer. Math. Soc., 2005, 488 pages. With an appendix by P. Exner.
Soliton Equations and Their Algebro-Geometric Solutions. Vol. I: (1+1)-Dimensional Continuous Models; with H. Holden, Cambridge Studies in Advanced Mathematics, Vol. 79, Cambridge Univ. Press, Cambridge, 2003, 505 pages.
Soliton Equations and Their Algebro-Geometric Solutions. Vol. II: (1+1)-Dimensional Discrete Models; with H. Holden, J. Michor, and G. Teschl, Cambridge Studies in Advanced Mathematics, Vol. 114, Cambridge Univ. Press, Cambridge, 2008, 438 pages.
Sturm—Liouville Operators, Their Spectral Theory, and Some Applications; with R. Nichols and M. Zinchenko, Colloquium Publications, Vol. 67, Amer. Math. Soc., Providence, RI, 2024, 927 pages.
Professional Honors
Alexander von Humboldt Fellowship (University of Bielefeld, Germany, 1980-81 and 1983-84).
Max Kade Fellowship (California Institute of Technology, Pasadena, CA, USA, 1987-88).
Ludwig Boltzmann Award (Austrian Physical Society) 1987.
Invited One Hour Address at the AMS Meeting at the Louisiana State University, Baton Rouge, LA, USA, April 1996.
Election to the Royal Norwegian Society of Science and Letters, Trondheim, Norway, January 1, 2002.
Fellow of the American Mathematical Society (inaugural class, January 1, 2013).
Honorary Doctorate, Technical University of Graz, Austria, 2020.
Fellow of the European Academy of Sciences, Mathematics Division (elected, September 2024) https://www.eurasc.eu/