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Keywords:
mean approximation; polyanalytic Besov space; polyanalytic Bergman space; dilatation; non-radial weight; angular weight
mean approximation; polyanalytic Besov space; polyanalytic Bergman space; dilatation; non-radial weight; angular weight
Summary:
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 $q$.
References:
[1] Abkar, A.: Norm approximation by polynomials in some weighted Bergman spaces. J. Funct. Anal. 191 (2002), 224-240. DOI 10.1006/jfan.2001.3851 | MR 1911185 | Zbl 1059.30049
[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 10.1007/s11785-021-01188-2 | MR 4357427 | Zbl 1485.30018
[3] Abkar, A.: Mean approximation in Bergman spaces of polyanalytic functions. Anal. Math. Phys. 12 (2022), Article ID 52, 16 pages. DOI 10.1007/s13324-022-00671-z | MR 4396660 | Zbl 1486.30130
[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 10.1007/978-3-319-01806-5_1 | MR 3203099 | Zbl 1318.30070
[5] Balk, M. B.: Polyanalytic Functions. Mathematical Research 63. Akademie, Berlin (1991). MR 1184141 | Zbl 0764.30038
[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 10.1112/blms/bdm026 | MR 2331575 | Zbl 1196.30046
[7] Haimi, A., Hedenmalm, H.: Asymptotic expansion of polyanalytic Bergman kernels. J. Funct. Anal. 267 (2014), 4667-4731. DOI 10.1016/j.jfa.2014.09.002 | MR 3275106 | Zbl 1310.30040
[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 0427648 | Zbl 0372.30034
[9] Muskhelishvili, N. I.: Some Basic Problems of the Mathematical Theory of Elasticity. Nauka, Moscow (1966), Russian. MR 0202367 | Zbl 0151.36201
[10] Ramazanov, A. K.: On the structure of spaces of polyanalytic functions. Math. Notes 72 (2002), 692-704. DOI 10.1023/A:1021469308636 | MR 1963139 | Zbl 1062.30055
[11] Vasilevski, N. L.: On the structure of Bergman and poly-Bergman spaces. Integral Equations Oper. Theory 33 (1999), 471-488. DOI 10.1007/BF01291838 | MR 1682807 | Zbl 0931.46023
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