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| Gerald B. Folland | |
|---|---|
| Name | Gerald B. Folland |
| Birth date | 1947 |
| Birth place | Boston, Massachusetts |
| Fields | Mathematics |
| Workplaces | Massachusetts Institute of Technology, University of Washington, University of Wisconsin–Madison, California Institute of Technology |
| Alma mater | Massachusetts Institute of Technology, Princeton University |
| Doctoral advisor | Elias M. Stein |
| Known for | Harmonic analysis, distributions, Fourier analysis, partial differential equations |
Gerald B. Folland is an American mathematician known for contributions to harmonic analysis, Fourier transform, and the theory of distributions. He has authored widely used textbooks and research papers that interface with topics in functional analysis, partial differential equations, and Lie groups. Folland's work has influenced researchers associated with institutions such as Princeton University, Massachusetts Institute of Technology, and the University of Washington.
Folland was born in Boston, Massachusetts and completed undergraduate studies at Massachusetts Institute of Technology before pursuing graduate study at Princeton University. At Princeton University he studied under Elias M. Stein, a central figure in modern harmonic analysis linked to work at Princeton and collaborations with scholars from Institute for Advanced Study and Harvard University. His doctoral work engaged techniques from Fourier transform, distribution theory, and classical analysis developed by predecessors at University of Chicago and University of California, Berkeley.
Folland held faculty positions at several major institutions, including the California Institute of Technology, the University of Wisconsin–Madison, and the University of Washington, where he influenced mathematics programs associated with American Mathematical Society activities and conferences at venues like Institute for Advanced Study and Mathematical Sciences Research Institute. He collaborated with researchers connected to Princeton University, Massachusetts Institute of Technology, and Harvard University, and participated in seminars resembling those at Courant Institute and IAS. His appointments intersected with visiting positions and lecture series at institutions such as Stanford University, Yale University, and University of Chicago.
Folland's research spans harmonic analysis, the theory of distributions, and applications to partial differential equations. He developed analyses related to the Fourier transform on Euclidean space and on Lie groups, extending techniques associated with Elias M. Stein, Lars Hörmander, and Norbert Wiener. His monographs synthesize material comparable to treatments by Stein, Hörmander, Reed and Simon, and Rudin, providing exposition that connects functional analysis with problems studied at institutions such as the Courant Institute and the Mathematical Sciences Research Institute. Folland contributed to the understanding of hypoelliptic operators, building on foundations laid by Lars Hörmander and linked to work on the Heisenberg group and representations studied by researchers from University of Chicago and Harvard University. His expository style influenced curricula at Princeton University and Massachusetts Institute of Technology and informed subsequent research by scholars at the Institute for Advanced Study and Stanford University.
Folland's publications and teaching earned recognition within communities associated with the American Mathematical Society, the Mathematical Association of America, and regional mathematical societies that organize meetings at locations such as Institute for Advanced Study and Mathematical Sciences Research Institute. He has been invited to lecture in series linked to Princeton University, Harvard University, and Massachusetts Institute of Technology and has served on editorial boards of journals connected to the American Mathematical Society and other professional organizations.
- Folland, G. B., "A Course in Abstract Harmonic Analysis", monograph used alongside texts by Elias M. Stein, Lars Hörmander, and Walter Rudin in graduate programs at Princeton University and Massachusetts Institute of Technology. - Folland, G. B., "Introduction to Partial Differential Equations", a text that complements works by Lawrence C. Evans and Lars Hörmander and is used in courses at Stanford University and University of Chicago. - Folland, G. B., research articles on the Fourier transform and distributions cited by authors affiliated with Institute for Advanced Study, Courant Institute, and Harvard University. - Folland, G. B., expository pieces and lecture notes circulated through seminars at Princeton University, Massachusetts Institute of Technology, and the Mathematical Sciences Research Institute.
Folland supervised graduate students and postdoctoral researchers who subsequently joined faculties at institutions such as Princeton University, University of Chicago, and Massachusetts Institute of Technology. He taught graduate courses that paralleled those offered by Elias M. Stein, Lars Hörmander, and Walter Rudin, contributing to doctoral training programs at Princeton University and the University of Washington. Folland also participated in committees and editorial boards associated with the American Mathematical Society and organized sessions at conferences held by the Mathematical Association of America and the Society for Industrial and Applied Mathematics.