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Euler calculus, Euler integral transforms, and combinatorial species / Huy Mai.
- Format:
- Book
- Thesis/Dissertation
- Author/Creator:
- Mai, Huy, author.
- Language:
- English
- Subjects (All):
- Mathematics.
- Mathematical functions.
- Data collection.
- Euclidean space.
- Mathematics--Penn dissertations.
- Penn dissertations--Mathematics.
- Local Subjects:
- Mathematics.
- Mathematical functions.
- Data collection.
- Euclidean space.
- Mathematics--Penn dissertations.
- Penn dissertations--Mathematics.
- Genre:
- Academic theses.
- Physical Description:
- 1 online resource (100 pages)
- Contained In:
- Dissertations Abstracts International 83-03B.
- Place of Publication:
- [Philadelphia, Pennsylvania] : University of Pennsylvania ; Ann Arbor : ProQuest Dissertations & Theses, 2021.
- Language Note:
- English
- System Details:
- Mode of access: World Wide Web.
- text file
- Summary:
- Euler integration is an integration theory with the Euler characteristic acting as the measure, and similar to classical analysis, it comes equipped with a collection of integral transforms. In this thesis, we focus on two such integral transforms: the persistent homology transform and the Fourier-Sato transform. We prove the invertibility of the former using the technique of Radon transform, and show the connection of the latter to Euler convolution and inner product. We also provide a new way to interpret the Euler integral through a generalization of combinatorial species, which also extends to magnitude homology and configuration spaces.
- Notes:
- Source: Dissertations Abstracts International, Volume: 83-03, Section: B.
- Advisors: Ghrist, Robert; Committee members: Block, Jonathan; Maximo, Davi.
- Department: Mathematics.
- Ph.D. University of Pennsylvania 2021.
- Local Notes:
- School code: 0175
- ISBN:
- 9798535590400
- Access Restriction:
- Restricted for use by site license.
- This item must not be sold to any third party vendors.
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