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On Fourier Transforms and Functional Equations on GL(2)

thesis
posted on 29.07.2022, 20:45 authored by William SokurskiWilliam Sokurski

We consider a novel setting for local harmonic analysis on reductive groups motivated by Langlands functoriality conjecture. To this end, we characterize certain non-linear Schwartz spaces on tori and reductive groups in spectral terms, and develop some of their structure in the unramified case, and we derive estimates of their moderate growth at infinity. We also consider non-linear Fourier transforms, and calculate their action on tame supercuspidal representations of $GL_2(F)$ in terms of inducing cuspidal data.

History

Degree Type

Doctor of Philosophy

Department

Mathematics

Campus location

West Lafayette

Advisor/Supervisor/Committee Chair

Freydoon Shahidi

Additional Committee Member 2

David Goldberg

Additional Committee Member 3

Tong Liu

Additional Committee Member 4

Baiying Liu

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