Finite sections of Segal-Bargmann space Toeplitz operators with polyradially continuous symbols

Böttcher, Albrecht; Wolf, Hartmut

doi:10.1090/S0273-0979-1991-16078-7

Authors: Albrecht Böttcher and Hartmut Wolf
Journal: Bull. Amer. Math. Soc. 25 (1991), 365-372
MSC (1985): Primary 47B35; Secondary 45L05
DOI: https://doi.org/10.1090/S0273-0979-1991-16078-7
MathSciNet review: 1090404
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Sheldon Axler, Bergman spaces and their operators, Surveys of some recent results in operator theory, Vol. I, Pitman Res. Notes Math. Ser., vol. 171, Longman Sci. Tech., Harlow, 1988, pp. 1–50. MR 958569
C. A. Berger and L. A. Coburn, Toeplitz operators and quantum mechanics, J. Funct. Anal. 68 (1986), no. 3, 273–299. MR 859136, DOI https://doi.org/10.1016/0022-1236%2886%2990099-6
C. A. Berger and L. A. Coburn, Toeplitz operators on the Segal-Bargmann space, Trans. Amer. Math. Soc. 301 (1987), no. 2, 813–829. MR 882716, DOI https://doi.org/10.1090/S0002-9947-1987-0882716-4
Albrecht Böttcher, Truncated Toeplitz operators on the polydisk, Monatsh. Math. 110 (1990), no. 1, 23–32. MR 1072725, DOI https://doi.org/10.1007/BF01571274
Albrecht Böttcher and Bernd Silbermann, The finite section method for Toeplitz operators on the quarter-plane with piecewise continuous symbols, Math. Nachr. 110 (1983), 279–291. MR 721280, DOI https://doi.org/10.1002/mana.19831100120
Albrecht Böttcher and Bernd Silbermann, Analysis of Toeplitz operators, Springer-Verlag, Berlin, 1990. MR 1071374
R. G. Douglas and Roger Howe, On the $C^ *$-algebra of Toeplitz operators on the quarterplane, Trans. Amer. Math. Soc. 158 (1971), 203–217. MR 288591, DOI https://doi.org/10.1090/S0002-9947-1971-0288591-1
I. C. Gohberg and I. A. Fel′dman, Convolution equations and projection methods for their solution, American Mathematical Society, Providence, R.I., 1974. Translated from the Russian by F. M. Goldware; Translations of Mathematical Monographs, Vol. 41. MR 0355675
A. V. Kozak, The reduction method for multidimensional discrete convolutions, Mat. Issled. 8 (1973), no. 3(29), 157–160, 184 (Russian). MR 0336426
V. S. Pilidi, Multidimensional bisingular operators, Dokl. Akad. Nauk SSSR 201 (1971), 787–789 (Russian). MR 0301578
I. B. Simonenko, Multidimensional discrete convolutions, Mat. Issled. 3 (1968), no. vyp. 1 (7), 108–122 (Russian). MR 0257763
Harold Widom, Asymptotic behavior of block Toeplitz matrices and determinants, Advances in Math. 13 (1974), 284–322. MR 409511, DOI https://doi.org/10.1016/0001-8708%2874%2990072-3