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Properties of p-adic C^k Distributions

Waller, Bradley A
http://rave.ohiolink.edu/etdc/view?acc_num=osu1385485834

Abstract Details

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.
Mathematics
number theory; p-adic analysis; p-adic measure theory; distributions; fourier transform; amice; p-adic functional analysis; p-adic distribution

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Citations

  • Waller, B. A. (2013). Properties of p-adic C^k Distributions [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1385485834

    APA Style (7th edition)

  • Waller, Bradley. Properties of p-adic C^k Distributions. 2013. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1385485834.

    MLA Style (8th edition)

  • Waller, Bradley. "Properties of p-adic C^k Distributions." Doctoral dissertation, Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1385485834

    Chicago Manual of Style (17th edition)

osu1385485834
591
© 2013, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.