THE POLYANALYTIC REPRODUCING KERNELS - Institut de Mathématiques de Marseille 2014- Access content directly
Preprints, Working Papers, ... Year : 2019



Let ν be a rotation invariant Borel probability measure on the complex plane having moments of all orders. Given a positive integer q, it is proved that the space of ν-square integrable q-analytic functions is the closure of q-analytic polynomials, and in particular it is a Hilbert space. We establish a general formula for the corresponding polyanalytic reproducing kernel. New examples are given and all known examples, including those of the analytic case are covered. In particular, weighted Bergman and Fock type spaces of polyanalytic functions are introduced. Our results have a higher dimensional generalization for measure on C p which are in rotation invariant with respect to each coordinate.
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Dates and versions

hal-01883849 , version 1 (28-09-2018)
hal-01883849 , version 2 (10-01-2019)


  • HAL Id : hal-01883849 , version 2


Hicham Hachadi, El Hassan Youssfi. THE POLYANALYTIC REPRODUCING KERNELS. 2019. ⟨hal-01883849v2⟩
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