About

Charles Fefferman is a mathematician whose research focuses on the extension of smooth functions, interpolation, and the analysis of linear operators in the context of function spaces such as C m,w. His work includes the development of sharp forms of Whitney's extension theorem, generalized Whitney theorems for jets, and the structure of linear operators for fitting C m -smooth functions to data. Fefferman's contributions also encompass the study of the C m norm of functions with prescribed jets, nearly optimal interpolation of data, and efficient algorithms for smooth data interpolation. His research advances the understanding of Whitney's extension problems, Sobolev extension, and the theoretical foundations of linear programming solutions for data fitting, reflecting a deep engagement with the mathematical analysis of smooth functions and their extensions.

Research topics

• Mathematics
• Mathematical analysis
• Mathematical economics
• Quantum mechanics
• Pure mathematics
• Condensed matter physics
• Physics
• Philosophy

Selected publications

• Simultaneous approximation in Lebesgue and Sobolev norms via eigenspaces

  Proceedings of the London Mathematical Society · 2022 · 34 citations

  1st authorCorresponding
  • Mathematics
  • Pure mathematics
  • Mathematical analysis

  We approximate functions defined on smooth bounded domains by elements of the eigenspaces of the Laplacian or the Stokes operator in such a way that the approximations are bounded and converge in both Sobolev and Lebesgue spaces. We prove an abstract result referred to fractional power spaces of positive, self-adjoint, compact-inverse operators on Hilbert spaces, and then obtain our main result by using the explicit form of these fractional power spaces for the Dirichlet Laplacian and Stokes operators. As a simple application, we prove that all weak solutions of the convective Brinkman–Forchheimer equations posed on a bounded domain in

  DOI

• Lower Bound on Quantum Tunneling for Strong Magnetic Fields

  SIAM Journal on Mathematical Analysis · 2022 · 18 citations

  1st authorCorresponding
  • Mathematics
  • Condensed matter physics
  • Quantum mechanics

  We consider a particle bound to a two-dimensional plane and a double-well potential, subject to a perpendicular uniform magnetic field. The energy difference between the lowest two eigenvalues---the eigenvalue splitting---is related to the tunneling probability between the two wells. We obtain upper and lower bounds on this splitting in the regime where both the magnetic field strength and the depth of the wells are large. The main step is a lower bound on the hopping amplitude between the wells, a key parameter in tight binding models of solid state physics, given by an oscillatory integral, whose phase has no critical point and which is exponentially small.

  DOI

• Elias M. Stein (1931–2018)

  Notices of the American Mathematical Society · 2021

  • Philosophy
  • Mathematical economics
  • Mathematics

  2018) had a profound influence on the field of analysis. He developed tools that are now indispensable, expanded and clarified major theories, and introduced new classes of questions that continue to stimulate research today. In addition, his singular skills as a mentor and expositor left a legacy of dozens of PhD students, hundreds of mathematical descendants, and thousands of loyal readers.

  PublisherDOI

• Miscellaneous back pages, Bull. Amer. Math. Soc. (N.S.), Volume 6, Number 1 (1982)

  Bulletin of the American Mathematical Society · 1982-01-01

  articleOpen access

  Soviet Mathematks-Doklady is a bimonthly translation journal containing the entire pure mathematics section of the DOKLADY AKADEMII NAUK SSSR.

  PublisherOA PDFDOI

• Miscellaneous back pages, Bull. Amer. Math. Soc. (N.S.), Volume 4, Number 1 (1981)

  Bulletin of the American Mathematical Society · 1981-01-01

  articleOpen access

  Soviet Mathematics-Doklady is a bimonthly translation journal containing the entire pure mathematics section of the DOKLADY AKADEMII NAUK SSSR.

  PublisherOA PDFDOI

Recent grants

• Fourier analysis and partial differential equations

  NSF · $687k · 2013–2017

• Fourier analysis and partial differential equations

  NSF · $450k · 2017–2022

• Topics in Analysis

  NSF · $739k · 2006–2010

• Fourier analysis and partial differential equations

  NSF · $959k · 2009–2013

Frequent coauthors

• Diego Córdoba

  91 shared

• Ángel Castro

  55 shared

• Francisco Gancedo

  43 shared

• Javier Gómez-Serrano

  Brown University

  40 shared

• Michael I. Weinstein

  38 shared

• José L. Rodrigo

  25 shared

• Garving K. Luli

  23 shared

• Luis Seco

  University of Toronto

  21 shared

Education

• Ph.D., Mathematics

  Princeton University

  1972

• B.S., Mathematics

  University of Chicago

  1967