Education

Doc. of Science	Mathematics	Sofia University	1983
Ph.D.	Mathematics	Sofia University	1977
B.S.	Mathematics	Sofia University	1972

Experience

1996 - 2022	Professor	University of South Carolina
2009 - 2018	Director	Interdisciplinary Math. Institute, USC
1986 - 1996	Professor	Bulgarian Academy of Sciences
1982 - 1986	Senior Research Fellow	Bulgarian Academy of Sciences
1977 - 1982	Research Fellow	Bulgarian Academy of Sciences

Courses Taught

Research

Dr. Petrushev is mainly interested in problems from Approximation Theory, Harmonic Analysis, and Numerical Analysis. In particular, he is interested in spaces of distributions such as Hardy, Besov and Triebel-Lizorkin spaces in harmonic, nonclassical, anisotropic and geometric settings as well as the construction of bases and frames for such spaces. Dr. Petrushev has obtained important results in nonlinear approximation from rational functions, splines, frames, ridge functions and other dictionaries. He is also interested in the applications of Approximation theory, including Geomagnetic and Geopotential field modeling. Dr. Petrushev is on the editorial boards of several prestigious mathematics journals: Foundations of Computational Mathematics, Constructive Approximation, SIAM Journal on Mathematical Analysis, Journal of Fourier Analysis and Applications, Transactions of Mathematics and Its Applications. His research has been supported by NSF, DOD/NGA, NEH, DARPA. Currently Dr. Petrushev has two active grants: (i) NSF-DMS-1714369: "Nonlinear approximation in geometric, harmonic and anisotropic settings with applications", 2017 - 2021, and (ii) NGA/DOD-HM04761812002: "Highly Effective Computational Methods in Geomagnetic Field Modeling", 2018 - 2023.

Selected Publications

• 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.
• G. Kerkyacharian, P. Petrushev, Y. Xu, Gaussian bounds for the weighted heat kernels on the interval, ball, and simplex, Constr. Approx. 51 (2020), no. 1, 73–122.
• A.G. Georgiadis, G. Kerkyacharian, G.Kyriazis, 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.
• G. Kerkyacharian, S. Ogawa, P. Petrushev, D. Picard, Regularity of Gaussian processes on Dirichlet spaces, Constr. Approx. 47 (2018), no. 2, 277–320.
• K.G. Ivanov, P. Petrushev, Harmonic Besov and Triebel-Lizorkin spaces on the ball, J. Fourier Anal. Appl. 23 (2017), no. 5, 1062–1096.
• S. Dekel, G. Kerkyacharian, G. Kyriazis, P. Petrushev, Hardy spaces associated with non-negative self-adjoint operators, Studia Math. 239 (2017), no. 1, 17–54.
• G. Kerkyacharian, P. Petrushev, Heat kernel based decomposition of spaces of distributions in the framework of Dirichlet spaces, Trans. Amer. Math. Soc. 367 (2015), no.1, 121-189.