Publications and Preprints

Articles

  1. Discretization of the Koch Snowflake Domain with Boundary and Interior Energies
    With Malcolm Gabbard, Carlos Lima, Gamal Mograby, Alexander Teplyaev
    To Appear in Fractals
  2. Geodesic Interpolation on Sierpinski Gaskets
    With Caitlin M. Davis, Laura A. LeGare, Cory W. McCartan
    Submitted
  3. BV functions and fractional Laplacians on Dirichlet spaces
    With Patricia Alonso Ruiz, Fabrice Baudoin, Li Chen, Nageswari Shanmugalingam, Alexander Teplyaev
    Submitted
  4. Harmonic Gradients on Higher Dimensional Sierpinski Gaskets
    With Luke Brown, Giovanni Ferrer, Gamal Mograby, Karuna Sangam
    To Appear in Fractals
  5. Spectral properties of graphs associated to the Basilica group
    With Antoni Brzoska, Courtney George, Samantha Jarvis, Alexander Teplyaev
    Submitted
  6. Besov class via heat semigroup on Dirichlet spaces III: BV functions and sub-Gaussian heat kernel estimate
    With Patricia Alonso-Ruiz, Fabrice Baudoin, Li Chen, Nageswari Shanmugalingam, Alexander Teplyaev
    Submitted
  7. Spectra of Magnetic Operators on the Diamond Lattice Fractal
    With Antoni Brzoska, Aubrey Coffey, Madeline Hansalik, Stephen Loew
    Submitted
  8. Besov class via heat semigroup on Dirichlet spaces II: BV functions and Gaussian heat kernel estimates
    With Patricia Alonso-Ruiz, Fabrice Baudoin, Li Chen, Nageswari Shanmugalingam, Alexander Teplyaev
    To Appear in Calc Var PDE
  9. Fractal AC circuits and propagating waves on fractals
    With Eric Akkermans, Joe P. Chen, Gerald Dunne and Alexander Teplyaev
    in Analysis, Probability and Mathematical Physics on Fractals, World Scientific 2020
  10. Besov class via heat semigroup on Dirichlet spaces I: Sobolev type inequalities
    with Patricia Alonso-Ruiz, Fabrice Baudoin, Li Chen, Nageswari Shanmugalingam, Alexander Teplyaev
    J. Funct. Anal. 278 (2020), no. 11, 108459
  11. The Strong Maximum Principle for Schrödinger operators on fractals
    With Marius V. Ionescu, Kasso A. Okoudjou
    Demonstr. Math. 52 (2019), no. 1, 404–409
  12. Sobolev Algebra Counterexamples
    With Thierry Coulhon
    J. Fractal Geom. 5 (2018), no. 2, 143–164.
  13. Embedding convex geometries and a bound on convex dimension
    With Michael Richter
    Discrete Math. 340 (2017), no. 5, 1059–1063.
  14. Power dissipation in fractal AC circuits
    With Joe P Chen, Loren Anderson, Ulysses Andrews, Antoni Brzoska, Aubrey Coffey, Hannah Davis, Lee Fisher, Madeline Hansalik, Stephen Loew and Alexander Teplyaev.
    J. Phys. A 50 (2017), no. 32, 325205
  15. Magnetic Laplacians of locally exact forms on the Sierpinski Gasket
    With Jessica Hyde, Daniel Kelleher, Jesse Moeller, Luis Seda
    Commun. Pure Appl. Anal. 16 (2017), no. 6, 2299–2319.
  16. Some spectral properties of pseudo-differential operators on the Sierpinski Gasket
    With Marius V. Ionescu and Kasso A. Okoudjou
    Proc. Amer. Math. Soc. 145 (2017), no. 5, 2183–2198.
  17. Magnetic fields on resistance spaces
    With Michael Hinz
    J. Fractal Geom. 3 (2016), no. 1, 75–93.
  18. Complex Powers of the Laplacian on Affine Nested Fractals as Calderón-Zygmund operators
    With Marius V. Ionescu
    Commun. Pure Appl. Anal. 13 (2014), no. 6, 2155–2175.
  19. Pseudo-differential Operators on Fractals
    With Marius V. Ionescu and Robert S. Strichartz
    Rev. Mat. Iberoam. 29 (2013), no. 4, 1159–1190.
  20. Derivations and Dirichlet forms on fractals
    With Marius V. Ionescu and Alexander Teplyaev
    J. Funct. Anal. 263 (2012), no. 8, 2141–2169.
  21. Estimates for the resolvent kernel of the Laplacian on p.c.f. self similar fractals and blowups
    Trans. Amer. Math. Soc. 364 (2012), no. 3, 1633–1685
  22. The resolvent kernel for PCF self-similar fractals
    by Marius Ionescu, Erin P. J. Pearse, Luke G. Rogers, Huo-Jun Ruan, Robert S. Strichartz
    Trans. Amer. Math. Soc. 362 (2010), no. 8, 4451–4479.
  23. Distribution theory on p.c.f. fractals
    With Robert S. Strichartz
    J. Anal. Math. 112 (2010), 137–191.
  24. Szegö limit theorems on the Sierpinski gasket
    With Kasso A. Okoudjou and Robert S. Strichartz
    J. Fourier Anal. Appl. 16 (2010), no. 3, 434–447.
  25. Laplacians on the basilica Julia set
    With Alexander Teplyaev.
    Commun. Pure Appl. Anal. 9 (2010), no. 1, 211–231.
  26. Smooth bumps, a Borel theorem and partitions of smooth functions on p.c.f. fractals.
    With Robert S. Strichartz and Alexander Teplyaev
    Trans. Amer. Math. Soc. 361 (2009), no. 4, 1765–1790.
  27. Gradients of Laplacian Eigenfunctions on the Sierpinski Gasket
    With Jessica L. DeGrado and Robert S. Strichartz
    Proc. Amer. Math. Soc. 137 (2009), no. 2, 531–540
  28. Generalized Eigenfunctions and a Borel Theorem on the Sierpinski Gasket
    With Kasso A Okoudjou and Robert S. Strichartz
    Canad. Math. Bull. 52 (2009), no. 1, 105–116.
  29. Unimodular Multipliers on Modulation Spaces.
    With Árpád Bényi, Kasso A. Okoudjou and Karlheniz Gröchenig
    J. Funct. Anal. 246 (2007), no. 2, 366–384
  30. Degree-independent Sobolev extension on locally uniform domains
    J. Funct. Anal. 235 (2006), no. 2, 619–665.

Book

Analysis, Probability and Mathematical Physics on Fractals
Edited with Patricia Alonso Ruiz, Joe P. Chen, Robert S. Strichartz and Alexander Teplyaev
Fractals and Dynamics in Mathematics, Science, and the Arts: Theory and Applications: Volume 5, World Scientific 2020

Other

  1. BV functions and Besov spaces associated with Dirichlet spaces
    With Patricia Alonso-Ruiz, Fabrice Baudoin, Li Chen, Nageswari Shanmugalingam and Alexander Teplyaev
    This has been broken into 3 papers.
  2. On a theorem of Grigorʹyan, Hu and Lau
    Unpublished note
  3. Detecting stable scales in images via non-smooth K-functionals
    With Triet M. Le
    UCLA Computational and Applied Mathematics Technical Report 10-63
  4. PhD Thesis: A degree-independent Sobolev extension operator
    Yale University