Pencho Petrushev
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Education
| Doc. of Sci. | Mathematics | Sofia University, Bulgaria | 1983 |
| Ph.D. | Mathematics | Sofia University, Bulgaria | 1977 |
| B.S. | Mathematics | Sofia University, Bulgaria | 1972 |
Experience
| 2009 – Present | Director | Interdisciplinary Mathematics Institute, Univ. of South Carolina |
| 1996 – Present | Professor | Department of Mathematics, Univ. of South Carolina |
| 1986 – 1996 | Professor | Inst. of Mathematics, Bulgarian Acad. of Sciences |
| 1982 – 1986 | Senior Research Fellow | Inst. of Mathematics, Bulgarian Acad. of Sciences |
| 1977 – 1982 | Research Fellow | Inst. of Mathematics, Bulgarian Acad. of Sciences |
Research
Research Interests
- Nonlinear approximation from rational functions, splines, and wavelets and related function spaces
- Nonlinear approximation from hierarchical anisotropic spline bases and associated Besov type spaces (B-spaces); algorithms for nonlinear spline approximation
- Approximation from ridge functions and in particular from neural networks
- Construction of bases and frames, consisting of e.g. rational functions, for Besov and Triebel-Lizorkin spaces
- Construction of frames and development of the Littlewood-Paley theory on the d-dimensional unit sphere and ball, and on the cube with Jacobi weights; nonlinear n-term approximation from such frames
- Construction of frames and development of the Littlewood-Paley theory in the framework of general Dirichlet spaces, and in particular on Riemannian manifolds and Lie groups
- Application of localized frames on the sphere to multiscale representation and approximation of the gravitational potential and in astrophysics
- Anisotropic spaces induced by anisotropic dilations of Rd and their frame decomposition
- Development of methods for voice assessment of high-speed videoendoscopy
- Reproduction of sound from optical sound tracks of motion picture films from digital scans
Current Projects
- Heat kernel based decomposition of spaces in the framework of Dirichlet spaces - This is a research project with Gerard Kerkyacharian, Laboratoire de Probabilites et Modeles Aleatoires, Universite Paris VI et Universite Paris VII. The main objective of the project is the construction of frames and development of the Littlewood-Paley theory in the setting of general Dirichlet spaces, and in particular on Lie groups and Riemannian manifolds.
- Reproduction of sound from optical sound tracks of motion picture films - This is a collaborative research project with Greg Wilsbacher from the USC Moving Image Research Collections (MIRC), Mark Cooper (Interim Director of MIRC) and Borislav Karaivanov (IMI Postdoc). We have a joint grant: "An Open Source Application for Image-Based Digital Reproduction of Optical Film Sound" (May 2011 - May 2014) from the National Endowment for the Humanities. The goal of this project is to develop an open-source software application to directly reproduce the optical sound tracks of motion picture films from digital scans. This is a part of the process of migration of the twentieth century film production into the digital realm with ultimate goal preservation of the twentieth-century’s cultural and historical record for future generations.
- Laryngeal High-Speed Videoendoscopy - This is a joint research project supported by NIH with Dimitar Deliyski (former Director of Voice and Speech Laboratory, Communication Sciences and Disorders, Arnold School of Public Health, USC, currently the Cotton Chair of Otolaryngology Research and Associate Director of the Communication Sciences Research Center at the Cincinnati Children's Hospital Medical Center). The primary purpose of this project is to develop methods for visualization and automatic measurement of vocal fold vibratory characteristics and the application of high-speed videoendoscopy in the medical diagnostic and functional evaluation of laryngeal pathology and voice disorders.
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Teaching Activities
Current Courses
- Math 751 - Mathematical Theory of Wavelets
Previous Courses
- Undergraduate courses: Calculus I (Math 141), Calculus II (Math 142), Vector Calculus (Math 241), Elementary Differential Equations (Math 242), Ordinary Differential Equations (Math 520), Linear Algebra (Math 544), Analysis I (Math 554), Analysis II (Math 555).
- Graduate courses: Analysis I (Math 703), Analysis II (Math 704), Applied Mathematics I (Math 720), Applied Mathematics II (Math 721), Approximation Theory (Math 725), Nonlinear Approximation (Math 729), Fourier Analysis (Math 750), Maximal Operators, Littlewood-Paley Theory, and Bases (Math 758P).
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Honors and Other Special Scientific Recognition
- The 2010 USC Educational Foundation Award for Research in Science, Mathematics, and Engineering
- The 2010 Manuel Garcia Prize from the International Association of Logopedics and Phoniatrics for outstanding contributions to the official journal of IALP and to the field of communication sciences and disorders, jointly with D. Deliyski, H. Bonilha, T. Gerlach, B. Martin-Harris, and R. Hillman
- The 1989 Bulgarian Mathematical Scienece Award "N. Obreshkov'' awarded by the Bulgarian Academy of Sciences and Sofia University
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Selected Publications
- A. Cohen, R. DeVore, P. Petrushev, and H. Xu, Nonlinear approximation and the space BV(R^2), Amer. J. Math. 121 (1999), 587-628.
- G. Kyriazis, P. Petrushev, New bases for Triebel-Lizorkin and Besov spaces, Trans. Amer. Math. Soc. 354 (2002), 749-776.
- B. Karaivanov, P. Petrushev, Nonlinear piecewise polynomial approximation beyond Besov spaces, Appl. Comput. Harmon. Anal. 15 (2003), No. 3, 177-223.
- F. Narcowich, P. Petrushev, and J. Ward, Decomposition of Besov and Triebel-Lizorkin spaces on the sphere, J. Funct. Anal. 238 (2006), 530-564.
- K. Ivanov, P. Petrushev, and Yuan Xu, Sub-exponentially localized kernels and frames induced by orthogonal expansions, Math. Z. 264 (2010), 361-397.
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IMI Preprints and Seminars
Go to the list of 38 preprints and 3 seminars by Pencho Petrushev.BACK TO TOP
