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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 $q$.
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

[1] Abkar, A.: Norm approximation by polynomials in some weighted Bergman spaces. J. Funct. Anal. 191 (2002), 224-240. | DOI | MR | JFM

[2] Abkar, A.: Approximation in weighted analytic Besov spaces and in generalized Fock spaces. Complex Anal. Oper. Theory 16 (2022), Article ID 11, 19 pages. | DOI | MR | JFM

[3] Abkar, A.: Mean approximation in Bergman spaces of polyanalytic functions. Anal. Math. Phys. 12 (2022), Article ID 52, 16 pages. | DOI | MR | JFM

[4] Abreu, L. D., Feichtinger, H. G.: Function spaces of polyanalytic functions. Harmonic and Complex Analysis and its Applications Trends in Mathematics. Springer, Cham (2014), 1-38. | DOI | MR | JFM

[5] Balk, M. B.: Polyanalytic Functions. Mathematical Research 63. Akademie, Berlin (1991). | MR | JFM

[6] Duren, P., Gallardo-Gutiérrez, E. A., Montes-Rodríguez, A.: A Paley-Wiener theorem for Bergman spaces with application to invariant subspaces. J. Lond. Math. Soc. 39 (2007), 459-466. | DOI | MR | JFM

[7] Haimi, A., Hedenmalm, H.: Asymptotic expansion of polyanalytic Bergman kernels. J. Funct. Anal. 267 (2014), 4667-4731. | DOI | MR | JFM

[8] Košelev, A. D.: On the kernel function of the Hilbert space of functions polyanalytic in a disk. Dokl. Akad. Nauk SSSR 232 (1977), 277-279 Russian. | MR | JFM

[9] Muskhelishvili, N. I.: Some Basic Problems of the Mathematical Theory of Elasticity. Nauka, Moscow (1966), Russian. | MR | JFM

[10] Ramazanov, A. K.: On the structure of spaces of polyanalytic functions. Math. Notes 72 (2002), 692-704. | DOI | MR | JFM

[11] Vasilevski, N. L.: On the structure of Bergman and poly-Bergman spaces. Integral Equations Oper. Theory 33 (1999), 471-488. | DOI | MR | JFM

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