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Harmonic Analysis and Representation Commons™
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Full-Text Articles in Harmonic Analysis and Representation
Numerical And Harmonic Analysis Of Simplex Number Parity, Hunter Dm Hannula
Numerical And Harmonic Analysis Of Simplex Number Parity, Hunter Dm Hannula
All NMU Master's Theses
The primary object of this thesis is the study of periodicity in the parity of simplex numbers by number-theoretic and harmonic methods. The regular d-simplex numbers are introduced geometrically, arithmetically, and combinatorially. We demonstrate that all sequences indexing even d-simplex numbers are defined by finitely many congruences in a single modulus, and are thus quasiperiodic. We therefore show that these "even index-sequences" are particular elements in an affine space of functions, providing a natural decomposition result. We then introduce the discrete Fourier transform to construct the periodic parts of each index sequence, enabling the development of explicit forms for the …
A Course In Harmonic Analysis, Jason Murphy
A Course In Harmonic Analysis, Jason Murphy
AOER Course Materials
These notes were written to accompany the courses Math 6461 and Math 6462 (Harmonic Analysis I and II) at Missouri University of Science & Technology during the 2018-2019 academic year. The goal of these notes is to provide an introduction to a range of topics and techniques in harmonic analysis, covering material that is interesting not only to students of pure mathematics, but also to those interested in applications in computer science, engineering, physics, and so on.