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Discrete convolution operators, the Fourier transformation, and its tropical counterpart: the Fenchel transformation
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Visual Information and Interaction. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction.
2017 (English)In: Proc. 3rd EAUMP Conference: Advances in Mathematics and its Applications, Kampala, Uganda: Makerere University , 2017, 7-28 p.Conference paper, Published paper (Other academic)
Abstract [en]

We study solvability of convolution equations for functions with discrete support in Rn, a special case being functions with support in the integer points. The more general case is of interest for special grids in Euclidean space, like the body-centered and face-centered tesselations of three-space.

The theorem of existence of fundamental solutions by de Boor, Höllig and Riemenschneider is generalized to general discrete supports using elementary methods. We also study the asymptotic growth of sequences and arrays using the Fourer and Fenchel transformations.

Discretization and tropicalization are two important procedures. I will pose a philosophical/mathematical problem in relation to them.

Place, publisher, year, edition, pages
Kampala, Uganda: Makerere University , 2017. 7-28 p.
Keyword [en]
Convolution operators, domains of holomorphy, discrete, tropical analysis, Fenchel transformation.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-331554OAI: oai:DiVA.org:uu-331554DiVA: diva2:1149277
Conference
Third EAUMP Conference, October 26–28, 2016, Makerere University, Kampala, Uganda
Note

Publication 17-6 at Kiselman's web site.

Available from: 2017-10-14 Created: 2017-10-14 Last updated: 2017-10-18

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