In this chapter we consider a differential operator (formula presented) associated to a real number μ acting on the space of formal power series, which may be regarded as the heat operator with respect to the radial coordinate in the 2μ-dimensional space for a positive integer μ. If λ is an integer, we show that (formula presented) carries Jacobi-like forms of weight λ to ones of weight λ + 2 and obtain the formula for the m-fold composite (formula presented) of such operators. We then determine the corresponding operators on modular series and as well as on automorphic pseudodifferential operators (cf. [72]).
CITATION STYLE
Choie, Y. J., & Lee, M. H. (2019). Heat operators. In Springer Monographs in Mathematics (pp. 91–106). Springer. https://doi.org/10.1007/978-3-030-29123-5_5
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