Pencho Petrushev

Selected Publications

  • K.G. Ivanov, P. Petrushev, Highly localized kernels on the sphere induced by Newtonian kernels, arXiv:1808.08637 pdf
  • A. Georgiadis, G. Kyriazis, and P. Petrushev, Product Besov and Triebel–Lizorkin spaces with application to nonlinear approximation, Constr. Approx. https://doi.org/10.1007/s00365-019-09490-1 pdf
  • K.G. Ivanov, P. Petrushev, Nonlinear spline approximation in BMO(R), CONSTRUCTIVE THEORY OF FUNCTIONS, Sozopol 2019 (B. Draganov, K. Ivanov, G. Nikolov and R. Uluchev, Eds.), pp. 73–112, Prof. Marin Drinov Publishing House, Sofia, 2020. pdf
  • G. Cleanthous, A. Georgiadis, G. Kerkyacharian, P. Petrushev, and D. Picard, Kernel and wavelet density estimators on manifolds and more general metric spaces, Bernoulli 26 (2020), no. 3, 1832–1862. pdf
  • K.G. Ivanov, P. Petrushev, Fast and accurate evaluation of geomagnetic field elements at arbitrary points in space, Geophys. J. Int. (2020) 224, 181–190. pdf
  • K.G. Ivanov, P. Petrushev, Nonlinear n-term approximation of harmonic functions from shifts of the Newtonian kernel, Trans. Amer. Math. Soc. 373 (2020), no. 5, 3117–3176. pdf
  • G. Kerkyacharian, P. Petrushev, and Yuan Xu, Gaussian bounds for the heat kernels on the ball and simplex: Classical approach, Studia Math. 250 (2020), no. 3, 235–252. pdf
  • G. Kerkyacharian, P. Petrushev, and Yuan Xu, Gaussian bounds for the weighted heat kernels on the interval, ball, and simplex, Constr. Approx. 51 (2020), no. 1, 73–122. pdf
  • A.G. Georgiadis, G. Kerkyacharian, G. Kyriazis, and P. Petrushev, Atomic and molecular decomposition of homogeneous spaces of distributions associated to non-negative self-adjoint operators, J. Fourier Anal. Appl. 25 (2019), no. 6, 3259–3309. pdf
  • G. Kerkyacharian, S. Ogawa, P. Petrushev, and D. Picard, Regularity of Gaussian processes on Dirichlet spaces, Constr. Approx. 47 (2018), 277–320. pdf
  • K. G. Ivanov, N. Pavlis, and P. Petrushev, Precise and efficient evaluation of gravimetric quantities at arbitrarily scattered points in space, Journal of Geodesy, 92 (2018), no. 7, 779–796. pdf
  • S. Dekel, G. Kerkyacharian, G. Kyriazis, and P. Petrushev, A New proof of the atomic decomposition of Hardy spaces, CONSTRUCTIVE THEORY OF FUNCTIONS, Sozopol 2016 (K. Ivanov, G. Nikolov and R. Uluchev, Eds.), pp. 59–73, Prof. Marin Drinov Academic Publishing House, Sofia, 2018. 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