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Szegö Limit Theorems on the Sierpiński Gasket

Abstract

We use the existence of localized eigenfunctions of the Laplacian on the Sierpiński gasket (SG) to formulate and prove analogues of the strong Szegö limit theorem in this fractal setting. Furthermore, we recast some of our results in terms of equally distributed sequences.

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Correspondence to Kasso A. Okoudjou.

Additional information

Communicated by Hans Feichtinger.

Research of the third author supported in part by the National Science Foundation, grant DMS-065440.

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Okoudjou, K.A., Rogers, L.G. & Strichartz, R.S. Szegö Limit Theorems on the Sierpiński Gasket. J Fourier Anal Appl 16, 434–447 (2010). https://doi.org/10.1007/s00041-009-9102-0

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  • DOI: https://doi.org/10.1007/s00041-009-9102-0

Keywords

  • Analysis on fractals
  • Equally distributed sequences
  • Laplacian
  • Localized eigenfunctions
  • Sierpiński gasket
  • Strong Szegö limit theorem

Mathematics Subject Classification (2000)

  • 35P20
  • 28A80
  • 42C99
  • 81Q10