Date of Award
2007
Level of Access Assigned by Author
Campus-Only Thesis
Degree Name
Master of Arts (MA)
Department
Mathematics
Advisor
William O. Bray
Second Committee Member
Andrew H. Knightly
Third Committee Member
David M. Bradley
Abstract
In a general sense, harmonic analysis is the study of decomposition and synthesis formulas for functions in terms of eigenfunctions to differential operators. Here the differential operator of interest is the Laplace-Beltrami operator. This differential operator is characterized by its invariance under isometries. In the settings of Euclidean space and real hyperbolic space, the rotation group is an important subgroup of isometries; its natural representation on the L2 Hilbert space of functions will decompose the latter into irreducible invariant subspaces. Bochner's identity arises from studying how the Fourier transform acts on these subspaces. The utility of the Bochner identity will then be demonstrated by considering versions of Hardy's theorem. Hardy's theorem comes from looking at special cases to the Uncertainty principle from quantum physics.
Recommended Citation
Smith, Zachary J., "The Bochner Identity in Harmonic Analysis" (2007). Electronic Theses and Dissertations. 1038.
https://digitalcommons.library.umaine.edu/etd/1038