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Properties of p-adic C^k Distributions

2013, Doctor of Philosophy, Ohio State University, Mathematics.
Distributions of $C^k$ functions over $\ZP$ have been characterized using formal power series by Amice. These characterizations allow us to find a sharp bound on the growth of $C^k$ distributions. In the case of $C^1$ distributions it is shown that two distributions that agree on the functions of the form $\chi_{a+p^n\ZP}$ have Fourier Transforms that differ by the product of the logarithm and the Fourier Transform of a measure.

The development of a Radon-Nikodym derivative is established for $C^1$ distributions under certain restrictions. This gives a result that is similar to a Lebesgue decomposition. This generalizes a theorem of Barbacioru.
Warren Sinnott (Advisor)
James Cogdell (Committee Member)
David Goss (Committee Member)
85 p.

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Waller, B. (2013). Properties of p-adic C^k Distributions. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Waller, Bradley. "Properties of p-adic C^k Distributions." Electronic Thesis or Dissertation. Ohio State University, 2013. OhioLINK Electronic Theses and Dissertations Center. 25 Sep 2017.

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Waller, Bradley "Properties of p-adic C^k Distributions." Electronic Thesis or Dissertation. Ohio State University, 2013. https://etd.ohiolink.edu/

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