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Exact boundary synchronization for a coupled system of 1-D wave equations with coupled boundary conditions of dissipative type
Hodge-de Rham theory on fractal graphs and fractals
1. | Reed College, Oregon, United States |
2. | Rice University, Texas, United States |
3. | Mathematics Department, Malott Hall, Cornell Univeristy, Ithaca, NY 14853, United States |
4. | The Chinese University of Hong Kong |
References:
[1] |
J. Azzam, M. Hall and R. S. Strichartz, Conformal energy, conformal Laplacian, and energy measures on the Sierpinski gasket,, Transactions of the American Mathematical Society, 360 (2008), 2089.
doi: 10.1090/S0002-9947-07-04363-2. |
[2] |
M. T. Barlow, "Diffusions on Fractals,", L.N.M. 1690, (1690), 1.
doi: 10.1007/BFb0092537. |
[3] |
J. Bello, Y. Li and R. S. Strichartz, Hodge-de Rham theory of k-forms on carpet type fractals,, in preparation., (). Google Scholar |
[4] |
F. Cipriani, Diriclet forms on noncommutative spaces,, L.N.M., (1954), 161.
doi: 10.1007/978-3-540-69365-9_5. |
[5] |
F. Cipriani, D Guido, T. Isola and J. Sauvageot, Spectral triples on the Sierpinski gasket,, in AMS Meeting, (2011). Google Scholar |
[6] |
F. Cipriani, D Guido, T, Isola and J. Sauvageot, Differential 1-forms, their integral and potential theory on the Sierpinski gasket,, arXiv:1105.1995., (). Google Scholar |
[7] |
F. Cipriani and J. Sauvageot, Derivations as square roots of Dirichlet forms,, J. Funct. Ana., 201 (2003), 78.
doi: 10.1016/S0022-1236(03)00085-5. |
[8] |
Colin de Verdière, "Spectres de graphes, Cours spécialisés,", vol. 4, (1998).
|
[9] |
M. Cucuringu and R. S. Strichartz, Self-similar energy forms on the Sierpinski gasket with twists,, Potential Anal., 27 (2007), 45.
doi: 10.1007/s11118-007-9047-3. |
[10] |
K. Dalrymple, R. S. Strichartz and J. P. Vinson, Fractal differential equations on the Sierpinski gasket,, J. Funct. Ana. and App., 5 (1999).
doi: 10.1007/BF01261610. |
[11] |
D Guido and T. Isola, Singular traces on semi-finite von Neumann algebras,, J. Funct. Ana., 134 (1995), 451.
doi: 10.1006/jfan.1995.1153. |
[12] |
D. Guido and T. Isola, Dimensions and singular traces for spectral triples, with applications to fractals,, J. Funct. Anal., 203 (2003), 362.
doi: 10.1016/S0022-1236(03)00230-1. |
[13] |
D. Guido and T. Isola, Dimensions and singular traces for spectral triples for fratcals in $\mathbbR^N$,, Advances in Operator Algebras and Mathematical Physics; Proceedings of the Conference held in Sinaia, (2003).
|
[14] |
M. Hinz, Limit chains on the Sierpinski gasket,, Indiana U. Math. J., ().
doi: 10.1512/iumj.2011.60.4404. |
[15] |
M. Ionescu, L. G. Rogers and A. Teplyaev, Derivations and Dirichlet forms on fractals,, arXiv:1106.1450., ().
doi: 10.1016/j.jfa.2012.05.021. |
[16] |
J. Kigami, "Anaysis on Fractals,", Cambridge Tracts in Mathematics, (2001).
doi: 10.1017/CBO9780511470943. |
[17] |
J. Owen and R. S. Strichartz, Boundary value problems for harmonic functions on a domain in the Sierpinski gasket,, Indiana U. Math. J., 61 (2012), 319.
doi: 10.1512/iumj.2012.61.4539. |
[18] |
R. Peirone, Existence of eigenforms on fractals with three vertices,, Proc. Royal Soc. Edinburgh, 137A (2007), 1073.
doi: 10.1017/S0308210505001137. |
[19] |
R. Peirone, Existence of eigenforms on nicely separated fractals,, Proc. of Symposia in Pure Math., (2008), 231.
|
[20] |
C. Sabot, Existence and uniqueness of diffusions on finitely ramified self-similar fractals,, Ann. Sci. \'Ecole Norm. Sup., 30 (1997), 605.
doi: 10.1016/S0012-9593(97)89934-X. |
[21] |
R. S. Strichartz, Taylor approximations on Sierpinski gasket type fractals,, J. Funct. Anal., 174 (2000), 76.
doi: 10.1006/jfan.2000.3580. |
[22] |
R. S. Strichartz, Harmonic mappings of the Sierpinski gasket to the circle,, Proceedings of the American Mathematical Society, 130 (2001), 805.
doi: 10.1090/S0002-9939-01-06243-8. |
[23] |
R. S. Strichartz, "Differential Equations on Fractals: A Tutorial,", Princeton Univ. Press, (2006).
|
[24] |
A. Teplyaev, Harmonic coordinates on fractals with finitely ramified cell structure,, Canadian Journal of Math., 60 (2008), 457.
doi: 10.4153/CJM-2008-022-3. |
show all references
References:
[1] |
J. Azzam, M. Hall and R. S. Strichartz, Conformal energy, conformal Laplacian, and energy measures on the Sierpinski gasket,, Transactions of the American Mathematical Society, 360 (2008), 2089.
doi: 10.1090/S0002-9947-07-04363-2. |
[2] |
M. T. Barlow, "Diffusions on Fractals,", L.N.M. 1690, (1690), 1.
doi: 10.1007/BFb0092537. |
[3] |
J. Bello, Y. Li and R. S. Strichartz, Hodge-de Rham theory of k-forms on carpet type fractals,, in preparation., (). Google Scholar |
[4] |
F. Cipriani, Diriclet forms on noncommutative spaces,, L.N.M., (1954), 161.
doi: 10.1007/978-3-540-69365-9_5. |
[5] |
F. Cipriani, D Guido, T. Isola and J. Sauvageot, Spectral triples on the Sierpinski gasket,, in AMS Meeting, (2011). Google Scholar |
[6] |
F. Cipriani, D Guido, T, Isola and J. Sauvageot, Differential 1-forms, their integral and potential theory on the Sierpinski gasket,, arXiv:1105.1995., (). Google Scholar |
[7] |
F. Cipriani and J. Sauvageot, Derivations as square roots of Dirichlet forms,, J. Funct. Ana., 201 (2003), 78.
doi: 10.1016/S0022-1236(03)00085-5. |
[8] |
Colin de Verdière, "Spectres de graphes, Cours spécialisés,", vol. 4, (1998).
|
[9] |
M. Cucuringu and R. S. Strichartz, Self-similar energy forms on the Sierpinski gasket with twists,, Potential Anal., 27 (2007), 45.
doi: 10.1007/s11118-007-9047-3. |
[10] |
K. Dalrymple, R. S. Strichartz and J. P. Vinson, Fractal differential equations on the Sierpinski gasket,, J. Funct. Ana. and App., 5 (1999).
doi: 10.1007/BF01261610. |
[11] |
D Guido and T. Isola, Singular traces on semi-finite von Neumann algebras,, J. Funct. Ana., 134 (1995), 451.
doi: 10.1006/jfan.1995.1153. |
[12] |
D. Guido and T. Isola, Dimensions and singular traces for spectral triples, with applications to fractals,, J. Funct. Anal., 203 (2003), 362.
doi: 10.1016/S0022-1236(03)00230-1. |
[13] |
D. Guido and T. Isola, Dimensions and singular traces for spectral triples for fratcals in $\mathbbR^N$,, Advances in Operator Algebras and Mathematical Physics; Proceedings of the Conference held in Sinaia, (2003).
|
[14] |
M. Hinz, Limit chains on the Sierpinski gasket,, Indiana U. Math. J., ().
doi: 10.1512/iumj.2011.60.4404. |
[15] |
M. Ionescu, L. G. Rogers and A. Teplyaev, Derivations and Dirichlet forms on fractals,, arXiv:1106.1450., ().
doi: 10.1016/j.jfa.2012.05.021. |
[16] |
J. Kigami, "Anaysis on Fractals,", Cambridge Tracts in Mathematics, (2001).
doi: 10.1017/CBO9780511470943. |
[17] |
J. Owen and R. S. Strichartz, Boundary value problems for harmonic functions on a domain in the Sierpinski gasket,, Indiana U. Math. J., 61 (2012), 319.
doi: 10.1512/iumj.2012.61.4539. |
[18] |
R. Peirone, Existence of eigenforms on fractals with three vertices,, Proc. Royal Soc. Edinburgh, 137A (2007), 1073.
doi: 10.1017/S0308210505001137. |
[19] |
R. Peirone, Existence of eigenforms on nicely separated fractals,, Proc. of Symposia in Pure Math., (2008), 231.
|
[20] |
C. Sabot, Existence and uniqueness of diffusions on finitely ramified self-similar fractals,, Ann. Sci. \'Ecole Norm. Sup., 30 (1997), 605.
doi: 10.1016/S0012-9593(97)89934-X. |
[21] |
R. S. Strichartz, Taylor approximations on Sierpinski gasket type fractals,, J. Funct. Anal., 174 (2000), 76.
doi: 10.1006/jfan.2000.3580. |
[22] |
R. S. Strichartz, Harmonic mappings of the Sierpinski gasket to the circle,, Proceedings of the American Mathematical Society, 130 (2001), 805.
doi: 10.1090/S0002-9939-01-06243-8. |
[23] |
R. S. Strichartz, "Differential Equations on Fractals: A Tutorial,", Princeton Univ. Press, (2006).
|
[24] |
A. Teplyaev, Harmonic coordinates on fractals with finitely ramified cell structure,, Canadian Journal of Math., 60 (2008), 457.
doi: 10.4153/CJM-2008-022-3. |
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