Dr. Rahul Garg
Associate Professor
rahulgarg@iiserb.ac.in
+91 755 269 1255
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
- 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.
Publication
| SNo | Authors | Title of Article | Pid | Journal | Year |
|---|---|---|---|---|---|
| 1 | Rahul Garg,Sundaram Thangavelu | Boundedness of certain linear operators on twisted Fock spaces | 5927 | Mathematische Zeitschrift | 2024 |
| 2 | Sayan Bagchi,Riju Basak,Rahul Garg,Abhishek Ghosh | On some operator-valued Fourier pseudo-multipliers associated to Grushin operators | 5931 | Journal of Mathematical Analysis and Applications | 2024 |
| 3 | Sayan Bagchi,Rahul Garg,Joydwip Singh | On extension of Calderón–Zygmund type singular integrals and their commutators | 6537 | Proc. Indian Acad. Sci. Math. Sci. | 2024 |
| 4 | Rahul Garg,Sayan Bagchi | On L2-boundedness of pseudo-multipliers associated to the Grushin operator | 5099 | Journal of Functional Analysis | 2024 |
| 5 | Sayan Bagchi,Riju Basak,Rahul Garg,Abhishek Ghosh | Sparse Bounds for Pseudo-multipliers Associated to Grushin Operators, II | 5109 | Journal of Geometric Analysis | 2024 |
| 6 | Abhishek Ghosh,Rahul Garg,Riju Basak,Sayan Bagchi | Sparse Bounds for Pseudo-multipliers Associated to Grushin Operators, I | 4707 | J. Fourier Anal. Appl. | 2023 |
| 7 | K. Jotsaroop,Rahul Garg | Localisation of Spectral Sums corresponding to the sub-Laplacian on the Heisenberg Group | 2555 | Indiana University Mathematics Journal | 2022 |
| 8 | Sundaram Thangavelu,Rahul Garg,Riju Basak | Homogeneous Fourier and Weyl multipliers on Sobolev spaces related to the Heisenberg group | 3097 | Journal of Functional Analysis | 2021 |
| 9 | Saurabh Shrivastava,Luz Roncal,Rahul Garg | Quantitative weighted estimates for Rubio de Francia's Littlewood-Paley square function | 2187 | Journal of Geometric Analysis | 2021 |
| 10 | Rahul Garg,Sundaram Thangavelu | Variations on a theorem of Beurling | 3873 | Adv. Pure Appl. Math. | 2015 |
| 11 | Rahul Garg,Daniel Spector | On the regularity of solutions to Poisson's equation | 3875 | Comptes Rendus Mathematique | 2015 |
| 12 | Rahul Garg,Amos Nevo,Krystal Taylor | The lattice point counting problem on the Heisenberg groups | 3877 | Ann. Inst. Fourier (Grenoble) | 2015 |
| 13 | Rahul Garg,Daniel Spector | On the role of Riesz potentials in Poisson's equation and Sobolev embeddings | 3879 | Indiana University Mathematics Journal | 2015 |
| 14 | Rahul Garg,Sundaram Thangavelu | On the structure of analytic vectors for the Schrödinger representation | 3871 | Monatsh. Math. | 2012 |
| 15 | Rahul Garg,Sundaram Thangavelu | On the Hermite expansions of functions from the Hardy class | 3869 | Studia Mathematica | 2010 |
