Sampling on the sierpinski gasket

Experimental Mathematics

Volumn 12, Issue 4, 2003, Pages 403-418

  Oberlin, Richard ^a   Street, Brian ^b   Strichartz, Robert S ^c  

^a FLORIDA STATE UNIVERSITY   (United States)

^b PRINCETON UNIVERSITY   (United States)

^c Department of Obstetrics Gynecology   (United States)

Author keywords

Analysis on fractals; Dirichlet kernel; Sampling theory; Sierpinski gasket; Spectral decimation

Indexed keywords

EID: 2442453664     PISSN: 10586458     EISSN: 1944950X     Source Type: Journal    
DOI: 10.1080/10586458.2003.10504509     Document Type: Article

References (15)

1. M. Barlow. “Diffusion on fractals.” In Lectures on Probability and Statistics, Lecture Notes Math., 1690, pp. 1-121. Berlin: Springer-Verlag, 1998.
2. M. Barlow and J. Kigami. “Localized Eigenfunctions of the Laplacian on p.c.f. Self-Similar Sets.” J. London Math. Soc. 56 (1997), 320-332.
3. O. Ben-Bassat, R. Strichartz, and A. Teplyaev. “What Is Not in the Domain of the Laplacian on Sierpinski Gasket Type Fractals.” Journal of Functional Analysis 166 (1999), 197-217.
4. J. J. Benedetto and P. J. S. G. Ferreira, editors. Modern Sampling Theory. Boston, MA: Birkhauser, 2001.
5. A. Cauchy. “Memoire sur diverses formules d’analyse.” Comptes Rendue Acad. Sci. Paris (12) (1841), 283-298; (reprinted in Oeuvres Complete d’Augustin Cauchy, Series 1, Vol. 6, Extract Number 118, 63-78, Paris: Gauthier-Villars, 1888)
6. K. Coletta, K. Dias, and R. Strichartz. “Numerical Analysis on the Sierpinski Gasket, with Applications to Schrodinger Equations, Wave Equation, and Gibbs’ Phenomenon.” Preprint, 2003.
7. K. Dalrymple, R. Strichartz, and J. Vinson. “Fractal Differential Equations on the Sierpinski Gasket.” J. Fourier Anal. Appl. 5 (1999), 203-284.
8. M. Fukushima and T. Shima. “On a Spectral Analysis for the Sierpinski Gasket.” Potential Anal. 1 (1992), 1-35.
9. M. Gibbons, A. Raj, and R. Strichartz. “The Finite Element Method on the Sierpinski Gasket.” Constructive Approx. 17 (2001), 561-588.
10. J. Kigami. “A Harmonic Calculus on the Sierpinski Gasket.” Japan J. Appl. Math. 6 (1989), 259-290
11. J. Kigami. Analysis on Fractals. Cambridge, UK: Cambridge University Press, 2001.
12. T. Shima. “On Eigenvalue Problems for Lapla- cians on p.c.f Self-Similar Sets.” Japan J. Indust. Appl. Math. 13 (1996), 1-23.
13. R. Strichartz. “Fractals in the Large.” Can. Math. J. 50 (1996), 638-657.
14. R. Strichartz. “Analysis on Fractals.” Notices American Mathematical Society 46 (1999), 1199-1208.
15. R. Strichartz and M. Usher. “Splines on Fractals.” Math. Proc. Cambridge Phil. Soc. 129 (2000), 331.