Journal of Mathematical Physics, Analysis, Geometry
2020, vol. 16, No 1, pp. 3-26     ( to contents , go back )

Toeplitz Operators with Radial Symbols on Bergman Space and Schatten-von Neumann Classes

Z. Bendaoud

Faculté des Sciences, Université Amar Telidji-Laghouat, B.P. 37G, route de Ghardaia, Laghouat 03000, Algérie

S. Kupin

Institut de Mathématiques de Bordeaux UMR5251, CNRS, Université de Bordeaux, 351 ave. de la Libération, 33405 Talence Cedex, France

K. Toumache

Faculté des Sciences Exactes, des Sciences de la Nature et de la Vie, Université Mohamed Khider-Biskra, B.P. 145, Biskra 07000, Algérie
E-mail: kamel

B. Touré

Faculté des Sciences et des Techniques, Université des Sciences, des Techniques et des Technologies de Bamako, Campus Universitaire de Badalabougou à Bamako, B.P. E-3206, Bamako, Mali

R. Zarouf

Institut de Mathématiques de Marseille, UMR 7373, Aix-Marseille Université, 39 rue F. Joliot Curie, 13453 Marseille Cedex 13, France

Received December 12, 2018, revised April 8, 2019.


In the present paper, we study spectral properties of Toeplitz operators with (quasi-) radial symbols on Bergman space. More precisely, the problem we are interested in is to understand when a given Toeplitz operator belongs to a Schatten-von Neumann class. The methods of the approximation theory (i.e., Legendre polynomials) are used to advance in this direction.

Mathematics Subject Classification 2000: 47B35, 30H20, 42C10.
Key words: Toeplitz operators, (quasi-) radial symbols, Bergman spaces, Schatten - von Neumann classes, Legendre polynomials.

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