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Department of Mathematics

Directory

Pencho Petrushev

Title: Professor
Department: Mathematics
College of Arts and Sciences
Email: pencho@math.sc.edu
Phone: 803-777-6686
Office: LeConte 427
Office Hours: T TH 4:15 – 5:15 pm
Resources: My Website
Curriculum Vitae

Interdisciplinary Mathematics Institute
 
Department of Mathematics
Pencho Petrushev

Education

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

Experience

1996 - Present 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

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
Matt 554: Analysis I
Matt 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

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 - 2020, and (ii) NGA/DOD-HM04761812002: "Highly Effective Computational Methods in Geomagnetic Field Modeling", 2018 - 2023.

Selected Publications

  • G. Kerkyacharian, S. Ogawa, P. Petrushev, D. Picard, Regularity of Gaussian processes on Dirichlet spaces, Constr. Approx. 47 (2018), no. 2, 277–320.
  • K. Ivanov, P. Petrushev, Harmonic Besov and Triebel-Lizorkin spaces on the ball, J. Fourier Anal. Appl. 23 (2017), no. 5, 1062–1096.
  • 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.
  • G. Kyriazis, P. Petrushev, Rational bases for spaces of holomorphic functions in the disc, J. Lond. Math. Soc. (2) 8 (2014), no. 2, 434-460.
  • K. Ivanov, P. Petrushev, Yuan Xu, Decomposition of spaces of distributions induced by tensor product bases, J. Funct. Anal. 263 (2012), no. 5, 1147-1197.

 


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