Geodesic
Polyanalytic Besov spaces and approximation by dilatations
Czechoslovak Mathematical Journal, Tome 74 (2024) no. 1, pp. 305-317.

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Using partial derivatives $\partial f / \partial z$ and $\partial f / \partial \bar {z}$, we introduce Besov spaces of polyanalytic functions in the open unit disk, as well as in the upper half-plane. We then prove that the dilatations of functions in certain weighted polyanalytic Besov spaces converge to the same functions in norm. When restricted to the open unit disk, we prove that each polyanalytic function of degree $q$ can be approximated in norm by polyanalytic polynomials of degree at most $q$.
DOI : 10.21136/CMJ.2023.0347-23
Classification : 30E10, 30H20, 30H25, 46E15
Keywords: mean approximation; polyanalytic Besov space; polyanalytic Bergman space; dilatation; non-radial weight; angular weight 
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Abkar, Ali. Polyanalytic Besov spaces and approximation by dilatations. Czechoslovak Mathematical Journal, Tome 74 (2024) no. 1, pp. 305-317. doi : 10.21136/CMJ.2023.0347-23. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2023.0347-23/

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