Research Interests

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, among others.

Education

• D.Sc. in Mathematics, Sofia University (1983)
• Ph.D. in Mathematics, Sofia University, (1977)
• B.S. in Mathematics, Sofia University, (1972)

Experience

• Professor, University of South Carolina (1996 – 2022)
• Director of the Interdisciplinary Mathematics Institute, University of South Carolina (2009 – 2018)
• Professor, Bulgarian Academy of Sciences (1986 – 1996)
• Senior Research Fellow, Bulgarian Academy of Sciences (1982 – 1986)
• Research Fellow, Bulgarian Academy of Sciences (1977 – 1982)

Courses Taught

• MATH 122: Calculus for Business Administration and Social Sciences
• MATH 141: Calculus I
• MATH 142: Calculus II
• MATH 241: Vector Calculus
• MATH 242: Elementary Differential Equations
• MATH 520: Ordinary Differential Equations I
• MATH 544: Linear Algebra
• MATH 550: Vector Analysis
• MATH 554: Analysis I
• MATH 703: Analysis I
• MATH 704: Analysis II
• MATH 720: Applied Mathematics I
• MATH 725: Approximation Theory
• MATH 729: Nonlinear Approximation Theory
• MATH 750: Fourier Analysis
• MATH 751: Wavelets
• MATH 758: Maximal Operators, Littlewood-Paley Theory, and Bases Research

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.