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Introduction
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2017 (English)In: Hyponormal Quantization of Planar Domains: Exponential Transform in Dimension Two, Springer, 2017, p. 1-5Chapter in book (Other academic)
Abstract [en]

This chapter offers an overview of the main interlacing themes, with emphasis on historical development and identification of the original sources. When looking at a picture through a mathematical lens, several intrinsic inner skeletons pop up. They are sometimes called in a suggestive and colorful way the “mother body”, or “madonna body”, or “the ridge”, or “caustic” of the original picture. Geometric or analytic features characterize these skeletons, but in general they remain very shy, displaying their shapes and qualitative features only after challenging technical obstacles are resolved. For example, the natural skeleton of a disk is its center, the interval between the foci of an ellipse stands out as a canonical ridge. For reasons to be discussed in these notes, the internal bisector segments in a triangle form its “mother body”. Disagreement starts with a sector of a disk, where the “bodies” (maternal, madonna type, or the one proposed below) are different. In the scenario outlined in these notes, a disjoint union of disks has their centers as a natural skeleton.

Place, publisher, year, edition, pages
Springer, 2017. p. 1-5
Series
Lecture Notes in Mathematics, ISSN 0075-8434 ; 2199
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-216718DOI: 10.1007/978-3-319-65810-0_1Scopus ID: 2-s2.0-85030709784ISBN: 9783319658094 (print)OAI: oai:DiVA.org:kth-216718DiVA, id: diva2:1153934
Note

QC 20171101

Available from: 2017-11-01 Created: 2017-11-01 Last updated: 2017-11-01Bibliographically approved

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