Geodesic
Spectral Properties of the Commutator of Bergman's Projection and the Operator of Multiplication by an Analytic Function
Canadian journal of mathematics, Tome 56 (2004) no. 2, pp. 277-292

Voir la notice de l'article provenant de la source Cambridge University Press

It is shown that the singular values of the operator $aP\,-\,Pa$ , where $P$ is Bergman's projection over a bounded domain $\Omega $ and $a$ is a function analytic on $\bar{\Omega }$ , detect the length of the boundary of $a\left( \Omega\right)$ . Also we point out the relation of that operator and the spectral asymptotics of a Hankel operator with an anti-analytic symbol.
DOI : 10.4153/CJM-2004-013-8
Mots-clés : 47B10 
Dostanić, Milutin R. Spectral Properties of the Commutator of Bergman's Projection and the Operator of Multiplication by an Analytic Function. Canadian journal of mathematics, Tome 56 (2004) no. 2, pp. 277-292. doi: 10.4153/CJM-2004-013-8
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[1] [1] Arazy, J., Fisher, S. D. and Janson, S., An identity for reproducing kernels in a planar domain and Hilbert-Schmidt Hankel operators. J. Reine Angew. Math. 406(1990), 179–199. Google Scholar

[2] [2] Arazy, J., Fisher, S. D. and Peetre, J., Hankel operators on weighted Bergman spaces. Amer. J. Math. 110(1988), 989–1054. Google Scholar

[3] [3] Birman, M. Š. and Solomjak, M. Z., Estimates of singular values of the integral operators. Uspekhi Mat. Nauk (193) 32(1977), 17–84. Google Scholar

[4] [4] Connes, A., Noncommutative Geometry. Academic Press, Inc., 1994. Google Scholar

[5] [5] Dostanić, M. R., Spectral properties of the Cauchy operator and its product with Bergman's projection on a bounded domain. Proc. LondonMath. Soc. (3) 76(1998), 667–684. Google Scholar

[6] [6] Gohberg, I. C. and Krein, M. G., Introduction to the theory of linear nonselfadjoint operators. Transl. Math. Monogr. , Amer. Math. Soc., Providence, R.I., 1969. Google Scholar

[7] Itogi nauki i tehniki, Contemporary problems in mathematics, Fundamental directions. , Moscow 1988, in Russian. Google Scholar

[8] [8] Leucking, D. H., Characterizations of Certain Classes of Hankel Operators on the Bergman Spaces of the Unit Disk. J. Funct. Anal. 110(1992), 247–271. Google Scholar

[9] [9] Nowak, K., Weak Type Estimate for Singular values of Commutator on Weighted Bergman Spaces. Indiana Univ.Math. J. (4) 40(1991), 1315–1331. Google Scholar

[10] [10] Nowak, M., Compact Hankel operators with conjugate analytic symbols. Rend. Circ. Mat. Palermo (2) 47(1998), 363–374. Google Scholar

[11] [11] Paraska, V. I., On asymptotics of eigenvalues and singular numbers of linear operators which increase smoothness. In: Russian Math. Sb. (NS) 68(1965), 623–631. Google Scholar

[12] [12] Range, R. M., Holomorphic functions and integral representations in several complex variables. Springer, Berlin, 1986. Google Scholar

[13] [13] Warschawski, S. E., Über das Randverhalten der Ableitung der Abbildungs-funktion bei konformer Abbildung. Math. Z. (3–4) 35(1932), 321–456. Google Scholar

[14] [14] Zhy, K., OperatorTheory in Function Spaces. Marcel Dekker INC., 1990. Google Scholar

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