Geodesic
On products of some Toeplitz operators on polyanalytic Fock spaces
Czechoslovak Mathematical Journal, Tome 70 (2020) no. 2, pp. 369-379 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The purpose of this paper is to study the Sarason's problem on Fock spaces of polyanalytic functions. Namely, given two polyanalytic symbols $f$ and $g$, we establish a necessary and sufficient condition for the boundedness of some Toeplitz products $ T_{f}T_{\bar g}$ subjected to certain restriction on $f$ and $g$. We also characterize this property in terms of the Berezin transform.
The purpose of this paper is to study the Sarason's problem on Fock spaces of polyanalytic functions. Namely, given two polyanalytic symbols $f$ and $g$, we establish a necessary and sufficient condition for the boundedness of some Toeplitz products $ T_{f}T_{\bar g}$ subjected to certain restriction on $f$ and $g$. We also characterize this property in terms of the Berezin transform.
DOI : 10.21136/CMJ.2019.0334-18
Classification : 30G30, 30H20, 46E22, 47B35
Keywords: polyanalytic function; Toeplitz operator; Fock space; Sarason's problem 
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Casseli, Irène. On products of some Toeplitz operators on polyanalytic Fock spaces. Czechoslovak Mathematical Journal, Tome 70 (2020) no. 2, pp. 369-379. doi: 10.21136/CMJ.2019.0334-18

[1] Abreu, L. D.: On the structure of Gabor and super Gabor spaces. Monatsh. Math. 161 (2010), 237-253. | DOI | MR | JFM

[2] Aleman, A., Pott, S., Reguera, M. C.: Sarason conjecture on the Bergman space. Int. Math. Res. Not. 2017 (2017), 4320-4349. | DOI | MR | JFM

[3] Askour, N., Intissar, A., Mouayn, Z.: Espaces de Bargmann généralisés et formules explicites pour leurs noyaux reproduisants. C. R. Acad. Sci., Paris, Sér. I, Math. 325 (1997), 707-712 French. | DOI | MR | JFM

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

[5] Bommier-Hato, H., Youssfi, E. H., Zhu, K.: Sarason's Toeplitz product problem for a class of Fock spaces. Bull. Sci. Math. 141 (2017), 408-442. | DOI | MR | JFM

[6] Cho, H. R., Park, J.-D., Zhu, K.: Products of Toeplitz operators on the Fock space. Proc. Am. Math. Soc. 142 (2014), 2483-2489. | DOI | MR | JFM

[7] Haimi, A., Hedenmalm, H.: The polyanalytic Ginibre ensembles. J. Stat. Phys. 153 (2013), 10-47. | DOI | MR | JFM

[8] Nazarov, F.: A counterexample to Sarason's conjecture. Available at http://users.math.msu.edu/users/fedja/prepr.html

[9] Sarason, D.: Exposed points in $H^1$. I. The Gohberg Anniversary Collection, Vol. II Operator Theory: Advances and Applications 41. Birkhäuser, Basel (1989), 485-496. | MR | JFM

[10] Sarason, D.: Products of Toeplitz operators. Linear and Complex Analysis. Problem Book 3, Part I V. P. Havin, N. K. Nikolskii Lecture Notes in Mathematics 1573. Springer, Berlin (1994), 318-319. | DOI | MR | JFM

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