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Title: On Homogeneous Distributions and Non-isotropic Dilations
Authors: Sardarli, Mariya
Advisors: Ionescu, Alexander
Contributors: Stein, Elias
Department: Mathematics
Class Year: 2015
Abstract: The aim of this thesis is to provide an introduction to the relationship between homogeneous distributions and the Fourier transform. We review the properties of isotropic dilations and demonstrates how they may be extended to non-isotropic dilations (x1, . . . , xd) 7→ (a α1 x1, . . . , aαd xd) with positive exponents αj . In the last chapter we drop the positive exponent condition in the dilation and explore the dilation (x1, x2) 7→ (ax1, a−1x2).
Extent: 33 pages
Type of Material: Princeton University Senior Theses
Language: en_US
Appears in Collections:Mathematics, 1934-2016

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