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Personal Details

Designation : Assistant Professor Department : Mathematics E-Mail : rahulgarg@iiserb.ac.in Phone : +91 755 269 1255, 669 1255 Fax : +91 755 669 2392



Academic Details


  • Assistant Professor (Oct 2015-), Mathematics, Indian Institute of Science Education and Research, Bhopal, India.
  • Postdoc (Nov 2012-Sep 2015), Technion - Israel Institute of Technology, Haifa, Israel.
  • Ph.D. (2007-2012), Indian Institute of Science, Bangalore, India.

    Research Interest


    • My research interests lie in the domain of Harmonic Analysis. So far I have focused on problems with the underlying space either Euclidean or the Heisenberg group. These include uncertainty principles of Hardy and Beurling in the Euclidean space, study of the Schrodinger representations of the Heisenberg group, and the lattice point counting problem in the Euclidean space and the Heisenberg group. These studies have also led me to some of the research problems in PDE (Partial Differential Equations). For example, we analyzed properties of Riesz potentials in the Euclidean space and their applications to Poisson's equation and Sobolev spaces. My recent interests also include Hardy and Hardy-Sobolev inequalities, and the mapping properties of various integral operators.

    Publications


    • (with S. Thangavelu), On the Hermite expansions of functions from the Hardy class, Studia Math. 198(2) (2010), 177-195.
    • (with S. Thangavelu), On the structure of analytic vectors for the Schr√∂dinger representation, Monatsh. Math. 167(1) (2012), 61-80.
    • (with S. Thangavelu), Variations on a theorem of Beurling, Adv. Pure Appl. Math. 6(3) (2015), 135-146.
    • (with D. Spector), On the regularity of solutions to Poisson's equation, C. R. Math. Acad. Sci. Paris 353(9) (2015), 819-823.
    • (with A. Nevo and K. Taylor), The lattice point counting problem on the Heisenberg groups, Ann. Inst. Fourier (Grenoble) 65(5) (2015), 2199-2233.
    • (with D. Spector), On the role of Riesz potentials in Poisson's equation and Sobolev embeddings, Indiana Univ. Math. J. 64(6) (2015), 1697-1719.