On polygonal measures with vanishing harmonic moments
2014 (English)In: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538, Vol. 123, 281-301 p.Article in journal (Refereed) Published
A polygonal measure is the sum of finitely many real constant density measures supported on triangles in a,. Given a finite set S aS, a,, we study the existence of polygonal measures spanned by triangles with vertices in S, all of whose harmonic moments vanish. We show that for generic S, the dimension of the linear space of such measures is . We also investigate the situation in which the density for such measure takes on only values 0 or +/- 1. This corresponds to pairs of polygons of unit density having the same logarithmic potential at a. We show that such (signed) measures do not exist for |S| a parts per thousand currency sign 5, but that for each n a parts per thousand yen 6 one can construct an S, with |S| = n, giving rise to such a measure.
Place, publisher, year, edition, pages
2014. Vol. 123, 281-301 p.
IdentifiersURN: urn:nbn:se:su:diva-107044DOI: 10.1007/s11854-014-0021-xISI: 000339826500010OAI: oai:DiVA.org:su-107044DiVA: diva2:743001