Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2010, Article ID 464815, 17 pages
http://dx.doi.org/10.1155/2010/464815
Research Article

Some Remarks on Diffusion Distances

1Theoretical and Applied Science, Ramapo College of NJ, 505 Ramapo Valley Road, Mahwah, NJ 07430, USA
2Mathematics Department, SUNY Rockland Community College, 145 College Road, Suffern, NY 10901, USA

Received 14 June 2010; Revised 31 July 2010; Accepted 3 September 2010

Academic Editor: Andrew Pickering

Copyright © 2010 Maxim J. Goldberg and Seonja Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Citations to this Article [5 citations]

The following is the list of published articles that have cited the current article.

  • Maxim J. Goldberg, and Seonja Kim, “An efficient tree-based computation of a metric comparable to a natural diffusion distance,” Applied and Computational Harmonic Analysis, vol. 33, no. 2, pp. 261–281, 2012. View at PublisherView at Google Scholar
  • A. Singer, and H.-T. Wu, “Vector diffusion maps and the connection Laplacian,” Communications on Pure and Applied Mathematics, vol. 65, no. 8, pp. 1067–1144, 2012. View at PublisherView at Google Scholar
  • William Leeb, and Ronald Coifman, “Hölder–Lipschitz Norms and Their Duals on Spaces with Semigroups, with Applications to Earth Mover’s Distance,” Journal of Fourier Analysis and Applications, 2015. View at PublisherView at Google Scholar
  • Maxim J. Goldberg, and Seonja Kim, “A Natural Diffusion Distance and Equivalence of Local Convergence and Local Equicontinuity for a General Symmetric Diffusion Semigroup,” Abstract and Applied Analysis, vol. 2018, pp. 1–9, 2018. View at PublisherView at Google Scholar
  • Maxim J. Goldberg, and Seonja Kim, “Equivalence of $$L_p$$ L p diffusion approximation and a function’s diffusion smoothness,” Semigroup Forum, 2019. View at PublisherView at Google Scholar