Selected Publications (Preprint Versions)


  • P. Petrushev, Approximation by ridge functions and neural networks, SIAM J. Math. Anal. 30 (1998), 155-189. pdf

  • A. Cohen, R. DeVore, P. Petrushev, and H. Xu, Nonlinear approximation and the space BV(R2), Amer. J. Math. 121 (1999), 587-628. pdf

  • P. Petrushev, Bases consisting of rational functions of uniformly bounded degrees or more general functions, J. Funct. Anal. 174 (2000), 18-75. pdf

  • G. Kyriazis, P. Petrushev, New bases for Triebel-Lizorkin and Besov spaces, Trans. Amer. Math. Soc. 354 (2002), no. 2, 749-776. pdf

  • P. Petrushev, Multivariate n-term rational and piecewise polynomial approximation, J. Approx. Theory, 121 (2003), 158-197. pdf

  • B. Karaivanov, P. Petrushev, Nonlinear piecewise polynomial approximation beyond Besov spaces, Appl. Comput. Harmon. Anal. 15 (2003), No. 3, 177-223. pdf

  • B. Karaivanov, P. Petrushev, and R. Sharpley, Algorithms for nonlinear piecewise polynomial approximation: Theoretical aspects, Trans. Amer. Math. Soc. 355 (2003), 2585-2631. pdf

  • P. Petrushev, Nonlinear n-term Approximation from Hierarchical Spline Bases, Constructive Theory of Functions, Varna 2002 (B. Bojanov, Ed.), DARBA, Sofia, 2003, pp. 33-85. pdf

  • O. Davydov, P. Petrushev, Nonlinear approximation from differentiable piecewise polynomials, SIAM J. Math. Anal. 35 (2004), 708-758. pdf

  • G. Kyriazis, K. Park, and P. Petrushev, B-spaces and their Characterization via Anisotropic Franklin Bases, Approximation Theory: a volume dedicated to Borislav Bojanov, 145-162, Prof. M. Drinov Acad. Publ. House, Sofia, 2004. pdf

  • M. Campos-Pinto, A. Cohen, and P. Petrushev, High order geometric smoothness for conservation laws, J. of Hyperbolic Differ. Equ. 2 (2005), 39-59. pdf

  • P. Petrushev, Anisotropic Spaces and Nonlinear n-term Spline Approximation, Approximation Theory XI: Gatlinburg 2004, 363-394, Mod. Methods Math., Nashboro Press, Brentwood, TN, 2005. pdf

  • P. Petrushev, Yuan Xu, Localized polynomial frames on the interval with Jacobi weights, J. Four. Anal. Appl. 11 (2005), 557-575. pdf

  • W. Dahmen, P. Petrushev, "Push-the-Error'' algorithm for nonlinear n-term approximation, Constr. Approx. 23 (2006), 261-304. pdf

  • G. Kyriazis, K. Park, and P. Petrushev, Anisotropic Franklin bases on polygonal domains, Math. Nachr. 279 (2006), 1099-1127. pdf

  • G. Kyriazis, P. Petrushev, On the construction of frames on Triebel-Lizorkin and Besov spaces, Proc. Amer. Math. Soc. 134 (2006), 1759-1770. pdf

  • F. J. Narcowich, P. Petrushev, and J. D. Ward, Localized Tight Frames on Spheres, SIAM J. Math. Anal. 38 (2006), 574-594. pdf

  • F. Narcowich, P. Petrushev, and J. Ward, Decomposition of Besov and Triebel-Lizorkin spaces on the sphere, J. Funct. Anal. 238 (2006), 530-564. pdf

  • W. Dahmen, S. Dekel, and P. Petrushev, Multilevel Preconditioning for Partition of Unity Methods - Some Analytic Concepts, Numer. Math. 107 (2007), 503-532. pdf

  • P. Petrushev, Yuan Xu, Localized polynomial frames on the ball, Constr. Approx. 27 (2008), 121-148. pdf

  • G. Kyriazis, P. Petrushev, and Yuan Xu, Jacobi decomposition of weighted Triebel-Lizorkin and Besov spaces, Studia Math. 186 (2008), 161-202. pdf

  • G. Kyriazis, P. Petrushev, and Yuan Xu, Decomposition of weighted Triebel-Lizorkin and Besov spaces on the ball, Proc. London Math. Soc. 97 (2008), 477-513. pdf

  • P. Petrushev, Yuan Xu, Decomposition of spaces of distributions induced by Hermite expansions, J. Fourier Anal. and Appl. 14 (2008), 372-414. pdf

  • G. Kerkyacharian, P. Petrushev, D. Picard, and Yuan Xu, Decomposition of Triebel-Lizorkin and Besov spaces in the context of Laguerre expansions, J. Funct. Anal. 256 (2009), 1137-1188. pdf

  • G. Kyriazis, P. Petrushev, On the construction of bases and frames for spaces of distributions, J. Funct. Anal. 257 (2009), 2159-2187. pdf

  • S. Dekel, Y. Han, and P. Petrushev, Anisotropic meshless frames on R^n, J. Fourier Anal. and Appl. 15 (2009), 634-662. pdf

  • S. Dekel, P. Petrushev, Anisotropic function spaces with applications, in "Multiscale, Nonlinear and Adaptive Approximation", Dedicated to W. Dahmen on the Occasion of his 60th Birthday, R. DeVore, A. Kunoth (Eds.), pp. 137-167, Springer, 2009. pdf

  • W. Dahmen, S. Dekel, and P. Petrushev, Two-level-split Decomposition of Anisotropic Besov Spaces, Constr. Approx. 31 (2010), no. 2, 149--194. pdf

  • G. Kerkyacharian, G. Kyriazis, E. Le Pennec, P. Petrushev and D. Picard, Inversion of noisy Radon transform by SVD based needlets, Appl. Comput. Harmon. Anal. 28 (2010), 24-45. pdf

  • K. Ivanov, P. Petrushev, and Yuan Xu, Sub-exponentially localized kernels and frames induced by orthogonal expansions, Math. Z. 264 (2010), 361-397. pdf

  • K. Ivanov, P. Petrushev, and Yuan Xu, Decomposition of spaces of distributions induced by tensor product bases, Math. Nachr. (to appear). pdf

  • K. Ivanov, P. Petrushev, Fast memory efficient evaluation of spherical polynomials at scattered points, preprint. pdf

  • G. Kyriazis, P. Petrushev, "Compactly" supported frames for spaces of distributions on the ball, preprint. pdf

  • G. Kyriazis, P. Petrushev, Rational bases for spaces of holomorphic functions in the disc, preprint. pdf