Dr. Rahul Garg

Harmonic Analysis

  • Designation : Associate Professor
  • Phone : +91 755 269 1255
                 
  • Email : rahulgarg@iiserb.ac.in
    • 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.
  • 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.
Authors Title of Article Journal Year
Sayan Bagchi
Riju Basak
Rahul Garg
Abhishek Ghosh
On some operator-valued Fourier pseudo-multipliers associated to Grushin operators
Details		 Journal of Mathematical Analysis and Applications 2024
Rahul Garg
Sundaram Thangavelu
Boundedness of certain linear operators on twisted Fock spaces
Details		 Mathematische Zeitschrift 2024
Sayan Bagchi
Riju Basak
Rahul Garg
Abhishek Ghosh
Sparse Bounds for Pseudo-multipliers Associated to Grushin Operators, II
Details		 Journal of Geometric Analysis 2024
Rahul Garg
Sayan Bagchi
On L2-boundedness of pseudo-multipliers associated to the Grushin operator
Details		 Journal of Functional Analysis 2024
Abhishek Ghosh
Rahul Garg
Riju Basak
Sayan Bagchi
Sparse Bounds for Pseudo-multipliers Associated to Grushin Operators, I
Details		 J. Fourier Anal. Appl. 2023
Rahul Garg
Daniel Spector
On the role of Riesz potentials in Poisson's equation and Sobolev embeddings
Details		 Indiana University Mathematics Journal 2015
Rahul Garg
Amos Nevo
Krystal Taylor
The lattice point counting problem on the Heisenberg groups
Details		 Ann. Inst. Fourier (Grenoble) 2015
Rahul Garg
Daniel Spector
On the regularity of solutions to Poisson's equation
Details		 Comptes Rendus Mathematique 2015
Rahul Garg
Sundaram Thangavelu
Variations on a theorem of Beurling
Details		 Adv. Pure Appl. Math. 2015
Rahul Garg
Sundaram Thangavelu
On the structure of analytic vectors for the Schrödinger representation
Details		 Monatsh. Math. 2012
Rahul Garg
Sundaram Thangavelu
On the Hermite expansions of functions from the Hardy class
Details		 Studia Mathematica 2010
Sundaram Thangavelu
Rahul Garg
Riju Basak
Homogeneous Fourier and Weyl multipliers on Sobolev spaces related to the Heisenberg group
Details		 Journal of Functional Analysis 2021
K. Jotsaroop
Rahul Garg
Localisation of Spectral Sums corresponding to the sub-Laplacian on the Heisenberg Group
Details		 Indiana University Mathematics Journal 2022
Saurabh Shrivastava
Luz Roncal
Rahul Garg
Quantitative weighted estimates for Rubio de Francia's Littlewood-Paley square function
Details		 Journal of Geometric Analysis 2021