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Articles 1 - 4 of 4
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 …
Local Limit Theorems On Finitely Generated Abelian Groups, Yutong Yan
Local Limit Theorems On Finitely Generated Abelian Groups, Yutong Yan
Honors Theses
In this thesis, we classify the pointwise behavior of finite-range random walks on finitely generated abelian groups in terms of local limit theorems. Random walks are central objects of research in probability theory, and the theory has found applications in statistics, physics, and even card shuffling. One significant topic in this line of study is random walks on finitely generated groups. Starting from the pioneering work of G. Pólya and H. Kesten, random walks on finitely generated groups have been studied extensively. However, many notable results on the subject (local limit theorems, for example) make assumptions about periodicity and irreducibility …
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.
A Non-Homogeneous, Spatio-Temporal, Wavelet Multiresolution Analysis And Its Application To The Analysis Of Motion, Thomas J. Burns
A Non-Homogeneous, Spatio-Temporal, Wavelet Multiresolution Analysis And Its Application To The Analysis Of Motion, Thomas J. Burns
Theses and Dissertations
This research presents a multiresolution wavelet analysis tool for analyzing motion in time sequential imagery. A theoretical framework is developed for constructing an L2R wavelet multiresolution analysis from three non-identical spatial and temporal L2R wavelet multiresolution analyses. This framework provides the flexibility to tailor the spatio-temporal frequency characteristics of the three dimensional wavelet filter to match the frequency behavior of the analyzed signal. An unconventional, discrete multiresolution wavelet decomposition algorithm is developed which yields a rich set of independent spatio-temporally oriented frequency channels for analyzing, the size and speed characteristics of moving objects. Unlike conventional wavelet decomposition methods, this algorithm …