Portrait of Hrushikesh Mhsakar

Hrushikesh Mhaskar is a research professor of mathematics at Claremont Graduate University who specializes in approximation theory, computational harmonic analysis, mathematics of data, and query processing.

In September 2016, in collaboration with Charles Chui at Stanford University, Mhaskar was awarded a three-year grant from the U.S. Army Research Office. The project aims to develop a unified theory of time-frequency analysis of signals that are stationary, nonlinear, and/or non-stationary, along with corresponding methods and computational schemes, that extend to both multi-directional and multivariate imaging. Past research has been supported by the National Science Foundation, the Air Force Office of Scientific Research, the National Security Agency, and the Research and Development Laboratories.

Mhaskar joined the mathematics faculty at California State University, Los Angeles, in the early 1980s and was promoted to full professor in 1990. He has published more than 100 journal articles in the areas of approximation theory, potential theory, neural networks, and wavelet analysis. His book, Weighted Polynomial Approximation, was published in 1997, while Fundamentals of Approximation Theory, co-authored with D. V. Pai, was published in 2000.

Mhaskar serves on the editorial boards of Journal of Approximation Theory, Jaen Journal on Approximation, and Forum d’Analyste. In addition, he was a co-editor of a special issue of Advances in Computational Mathematics devoted to mathematical aspects of neural networks, as well as on two edited collections of research articles: Wavelet Analysis and Applications and Frontiers in Interpolation and Approximation.

Mhaskar has held visiting positions and given invited lectures throughout North America, Europe, and Asia. He was awarded the Humboldt Fellowship for research in Germany four times and has been listed in Outstanding Young Men of America (1985) and Who’s Who in America’s Teachers (1994).

Mhaskar did his undergraduate studies in Institute of Science, Nagpur, and received his first M.Sc. in mathematics from the Indian Institute of Technology in Mumbai in 1976. He received his PhD in mathematics and MS in computer science from the Ohio State University, Columbus, in 1980.

“Wiener type theorems for Jacobi series with nonnegative coefficients”; Accepted for publication in Proceedings of the American Mathematical Society (With S. Tikhonov).

“A Generalized Diffusion Frame for Parsimonious Representation of Functions on Data Defined Manifolds.” Neural Networks 24 (2011): 345–59.

Co-authored with F. Filber. “Marcinkiewicz–Zygmund Measures on Manifolds.” Journal of Complexity 27 no.6 (2011): 568–96.

Co-authored with F. Filbir and J. Prestin “On the Problem of Parameter Estimation in Exponential Sums” Accepted  for publication in Constructive Approximation.

Co-authored with S. Chandrasekaran and K.R. Jayaraman. “Minimum Sobolev Norm Interpolation with Trigonometric Polynomials on the Torus.” Submitted for publication.

Co-authored with C.K. Chui. “Smooth Function Extension Based on High Dimensional Unstructured Data.” Submitted for publication.

Function Approximation on Large Unstructured Data Sets