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Generalized Eigenfunctions and a Borel Theorem on the Sierpinski Gasket

Open Access article
 Printed: Mar 2009
  • Kasso A. Okoudjou
  • Luke G. Rogers
  • Robert S. Strichartz
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We prove there exist exponentially decaying generalized eigenfunctions on a blow-up of the Sierpinski gasket with boundary. These are used to show a Borel-type theorem, specifically that for a prescribed jet at the boundary point there is a smooth function having that jet.
MSC Classifications: 28A80, 31C45 show english descriptions Fractals [See also 37Fxx]
Other generalizations (nonlinear potential theory, etc.)
28A80 - Fractals [See also 37Fxx]
31C45 - Other generalizations (nonlinear potential theory, etc.)

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