Riju Basak, Der-Chen Chang, Jonathan Riess, Jen-Chih Yao, Beta function formalism for Grushin operators (2)

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DOI: 10.23952/jnva.10.2026.4.01

Volume 10, Issue 4, 1 August 2026, Pages 703-733

Abstract. In this paper, we revisit the Grushin operator $\Delta_G = \frac{1}{2}(\partial_x^2 + x^{2k}\partial_y^2),$ $k \geq 1$ and study various geometric properties associated with the Grushin manifold. In particular, we employ a Beta function formalism to derive the heat kernel for the step~2 Grushin operator $\Delta_G = \frac{1}{2}(\partial_x^2 + x^2\partial_y^2).$ This approach is novel and proves to be effective in the analysis of the Grushin operator. Furthermore, the results presented here reaffirm existing findings in the literature.

How to Cite this Article:
R. Basak, D.C. Chang, J. Riess, J.C. Yao, Beta function formalism for Grushin operators (2), J. Nonlinear Var. Anal. 10 (2026), 703-733.