Selected Publications (Preprint Versions)
P. Petrushev,
Approximation by ridge functions and neural networks,
SIAM J. Math. Anal. 30 (1998), 155-189.
ps
pdf
A. Cohen, R. DeVore, P. Petrushev, and H. Xu,
Nonlinear approximation and the space BV(R2),
Amer. J. Math. 121 (1999), 587-628.
ps
pdf
P. Petrushev,
Bases consisting of rational functions of uniformly
bounded degrees or more general functions,
J. Funct. Anal. 174 (2000), 18-75.
ps
pdf
G. Kyriasis, P. Petrushev,
New bases for Triebel-Lizorkin and Besov spaces,
Trans. Amer. Math. Soc. 354 (2002), no. 2, 749-776.
ps
pdf
P. Petrushev,
Multivariate n-term rational and piecewise polynomial approximation,
J. Approx. Theory, 121 (2003), 158-197.
ps
pdf
B. Karaivanov, P. Petrushev,
Nonlinear piecewise polynomial approximation beyond Besov spaces,
Appl. Comput. Harmon. Anal. 15 (2003), No. 3, 177-223.
ps
pdf
B. Karaivanov, P. Petrushev, and R. Sharpley,
Algorithms for nonlinear piecewise polynomial approximation:
Theoretical aspects,
Trans. Amer. Math. Soc. 355 (2003), 2585-2631.
ps
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.
ps
pdf
O. Davydov, P. Petrushev,
Nonlinear approximation from differentiable piecewise polynomials,
SIAM J. Math. Anal. 35 (2004), 708-758.
ps
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.
ps
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.
ps
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.
ps
pdf
P. Petrushev, Yuan Xu,
Localized polynomial frames on the interval with Jacobi weights,
J. Four. Anal. Appl. 11 (2005), 557-575.
ps
pdf
W. Dahmen, P. Petrushev,
"Push-the-Error'' algorithm for nonlinear n-term approximation,
Constr. Approx. 23 (2006), 261-304.
ps
pdf
G. Kyriazis, K. Park, and P. Petrushev,
Anisotropic Franklin bases on polygonal domains,
Math. Nachr. 279 (2006), 1099-1127.
ps
pdf
G. Kyriazis, P. Petrushev,
On the construction of frames on Triebel-Lizorkin and Besov spaces,
Proc. Amer. Math. Soc. 134 (2006), 1759-1770.
ps
pdf
F. J. Narcowich, P. Petrushev, and J. D. Ward,
Localized Tight Frames on Spheres,
SIAM J. Math. Anal. 38 (2006), 574-594.
ps
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.
ps
pdf
P. Petrushev, Yuan Xu,
Localized polynomial frames on the ball,
preprint.
ps
pdf
W. Dahmen, S. Dekel, and P. Petrushev,
Multilevel Preconditioning for Partition of Unity Methods
- Some Analytic Concepts, preprint.
ps
pdf
G. Kyriazis, P. Petrushev, and Yuan Xu,
Jacobi decomposition of weighted Triebel-Lizorkin and Besov spaces,
preprint.
ps
pdf
W. Dahmen, P. Petrushev, and S. Dekel,
Two-level-split Decomposition of Anisotropic Besov Spaces,
preprint.
ps
pdf
G. Kyriazis, P. Petrushev, and Yuan Xu,
Decomposition of weighted Triebel-Lizorkin and Besov spaces on the ball,
preprint.
ps
pdf
P. Petrushev, Yuan Xu,
Decomposition of spaces of distributions induced by Hermite expansions,
preprint.
ps
pdf
G. Kerkyacharian, P. Petrushev, D. Picard, and Yuan Xu,
Decomposition of Triebel-Lizorkin and Besov spaces
in the context of Laguerre expansions,
preprint.
ps
pdf