Tube volumes via functional equations

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DENİZ A., Koçak Ş., ÖZDEMİR Y., ÜREYEN A. E.

Journal of Geometry, cilt.106, sa.1, ss.153-162, 2015 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 106 Sayı: 1
  • Basım Tarihi: 2015
  • Doi Numarası: 10.1007/s00022-014-0241-3
  • Dergi Adı: Journal of Geometry
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.153-162
  • Anahtar Kelimeler: Tube formulas, self-similar sprays, functional equations, Mellin transform
  • Anadolu Üniversitesi Adresli: Evet

Özet

© 2014, Springer Basel AG.Tube formulas for convex sets and for smooth submanifolds of Euclidean spaces have long been of interest for geometers. In the last two decades there has been great progress on tube formulas for badly behaved spaces such as fractals, sprays and strings. We give a new, simple proof of an interesting tube formula of M. Lapidus and E. Pearse for self-similar sprays using a natural functional equation satisfied by tube volumes of them.