BETA FUNCTION FORMALISM FOR GRUSHIN OPERATORS (2)

Basak, Riju

doi:10.23952/jnva.10.2026.4.01

BETA FUNCTION FORMALISM FOR GRUSHIN OPERATORS (2)

2026-01-01

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DOI：10.23952/jnva.10.2026.4.01

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Abstract

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In this paper, we revisit the Grushin operator AG = 12(partial derivative x 2 +x2k partial derivative y2 ), k >= 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 AG = 12(partial derivative x 2 +x2 partial derivative y2 ). 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.

Keywords:

Beta function theory

Heat kernel

Horizontal vector fields

Hamilton-Jacobi mechanics

Grushin operator

Missing directions

BETA FUNCTION FORMALISM FOR GRUSHIN OPERATORS (2)

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