Pencho Petrushev

Selected Publications

  • G. Kerkyacharian, S. Ogawa, P. Petrushev, and D. Picard, Regularity of Gaussian Processes on Dirichlet spaces, preprint.pdf
  • S. Dekel, G. Kerkyacharian, G. Kyriazis, and P. Petrushev, A new proof of the atomic decomposition of Hardy spaces, preprint.pdf
  • K. Ivanov, P. Petrushev, Harmonic Besov and Triebel-Lizorkin spaces on the ball, J. Fourier Anal. Appl. 23 (2017), no. 5, 1062–1096.pdf
  • S. Dekel, G. Kerkyacharian, G. Kyriazis, and P. Petrushev, Hardy spaces associated with non-negative self-adjoint operators, Studia Math. 239 (2017), no. 1, 17–54.pdf
  • M. Lind, P. Petrushev, Nonlinear nonnested spline approximation, Constr. Approx. 45 (2017), no. 2, 143–191.pdf
  • A. G. Georgiadis, G. Kerkyacharian, G. Kyriazis, P. Petrushev, Homogeneous Besov and Triebel-Lizorkin spaces associated to non-negative self-adjoint operators, J. Math. Anal. Appl. 449 (2017), no. 2, 1382–1412.pdf
  • K. Ivanov, P. Petrushev, Highly effective stable evaluation of bandlimited functions on the sphere, Numer. Algorithms, 71 (2016), no. 3, 585–611. pdf
  • K. Ivanov, P. Petrushev, Fast memory efficient evaluation of spherical polynomials at scattered points, Adv. Comput. Math. 41 (2015), 191–230. pdf
  • G. Kerkyacharian, P. Petrushev, Heat kernel based decomposition of spaces of distributions in the framework of Dirichlet spaces, Trans. Amer. Math. Soc. 367 (2015), 121–189. pdf
  • S. Dekel, G. Kerkyacharian, G. Kyriazis, and P. Petrushev, Compactly supported frames for spaces of distributions associated with nonnegative self-adjoint operators, Studia Math. 225 (2014), 115–163. pdf
  • G. Kyriazis, P. Petrushev, Rational bases for spaces of holomorphic functions in the disc, J. Lond. Math. Soc. (2) 89 (2014), 434–460. pdf
  • K. Ivanov, P. Petrushev, Irregular sampling of band-limited functions on the sphere, Appl. Comput. Harmon. Anal. 37 (2014), 545–562. pdf
  • T. Coulhon, G. Kerkyacharian, and P. Petrushev, Heat Kernel Generated Frames in the Setting of Dirichlet Spaces, J. Fourier Anal. Appl. 18 (2012), 995–1066. pdf
  • K. Ivanov, P. Petrushev, and Yuan Xu, Decomposition of spaces of distributions induced by tensor product bases, J. Funct. Anal. 263 (2012), 1147–1197. pdf
  • G. Kyriazis, P. Petrushev, "Compactly'' supported frames for spaces of distributions on the ball, Monatsh. Math. 165 (2012), 365–391. pdf
  • S. Dekel, P. Petrushev, and T. Weissblat, Hardy spaces on R^n with pointwise variable anisotropy, J. Fourier Anal. and Appl. 17 (2011), 1066–1107. 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
  • 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
  • W. Dahmen, S. Dekel, and P. Petrushev, Two-level-split Decomposition of Anisotropic Besov Spaces, Constr. Approx. 31 (2010), 149–19. pdf
  • G. Kyriazis, P. Petrushev, On the construction of bases and frames for spaces of distributions, J. Funct. Anal. 257 (2009), 2159–2187. 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
  • S. Dekel, Y. Han, and P. Petrushev, Anisotropic meshless frames on R^n, J. Fourier Anal. and Appl. 15 (2009), 634–662. pdf
  • P. Petrushev, Yuan Xu, Decomposition of spaces of distributions induced by Hermite expansions, J. Fourier Anal. and Appl. 14 (2008), 372–414. 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
  • G. Kerkyacharian, P. Petrushev, D. Picard, and T. Willer, Needlet algorithm for estimations in inverse problems, Electronic Journal of Statistics, 1 (2007), 30–76. 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
  • 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. Narcowich, P. Petrushev, and J. Ward, Decomposition of Besov and Triebel-Lizorkin spaces on the sphere, J. Funct. Anal. 238 (2006), 530–564. pdf
  • F. J. Narcowich, P. Petrushev, and J. D. Ward, Localized Tight Frames on Spheres, SIAM J. Math. Anal. 38 (2006), 574–594. 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
  • 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, Y. Xu, Localized polynomial frames on the interval with Jacobi weights, J. Fourier Anal. and Appl. 11 (2005), 557–575. pdf
  • O. Davydov, P. Petrushev, Nonlinear approximation from differentiable piecewise polynomials, SIAM J. Math. Anal. 35 (2003), 708–758. pdf
  • B. Karaivanov, P. Petrushev, Nonlinear piecewise polynomial approximation beyond Besov spaces, Appl. Comput. Harmon. Anal. 15 (2003), 177–223. pdf
  • B. Karaivanov, P. Petrushev, and R. Sharpley, Nonlinear piecewise polynomial approximation: Algorithms, Trans. Amer. Math. Soc. 355 (2003), 2585–2631. pdf
  • P. Petrushev, Multivariate n-term rational and piecewis polynomial approximation, J. Approx. Theory, 121 (2003), 158–197. pdf
  • G. Kyriazis, P. Petrushev, New bases for Triebel-Lizorkin and Besov spaces, Trans. Amer. Math. Soc. 354 (2002), 749–776. pdf
  • P. Petrushev, Bases consisting of rational function of uniformly bounded degrees or more general functions, J. Funct. Anal. 174 (2000), 18–75. pdf
  • A. Cohen, R. DeVore, P. Petrushev, and H. Xu, Nonlinear, Approximation and the space BV(R^2), Amer. J. Math. 121 (1999), 587–628. pdf
  • P. Petrushev, Approximation by ridge functions and neural networks, SIAM J. Math. Anal. 30 (1998), 155–189. pdf