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Heat Operators

  • YoungJu ChoieEmail author
  • Min Ho Lee
Chapter
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

In this chapter we consider a differential operator \( \mathcal{D}_{\mu }^{X} \) 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 \( \mathcal{D}_{\mu }^{X} \) carries Jacobi-like forms of weight λ to ones of weight λ + 2 and obtain the formula for the m-fold composite \( (\mathcal{D}_{\mu }^{X} )^{[m]} \) of such operators. We then determine the corresponding operators on modular series and as well as on automorphic pseudodifferential operators (cf. [72]).

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.MathematicsPohang University of Science and Technology (POSTECH)PohangKorea (Republic of)
  2. 2.University of Northern IowaCedar FallsUSA

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