# Department of **Mathematics**

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- Pencho Petrushev

## Directory

## Pencho Petrushev

Title: |
Distinguished Professor Emeritus |

Department: |
Mathematics College of Arts and Sciences |

Office: |
LeConte 414 |

Resources: |
My Website Curriculum Vitae |

#### 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.