On Some Problems for Reproducing Kernel Hilbert Space Operators via the Berezin Transform

被引：10
|
作者：
Karaev, M. T. [1 ,2 ]
Tapdigoglu, R. [3 ]
机构：
[1] Natl Acad Sci Azerbaijan, Inst Math & Mech, B Vagabzade Str 9, Baku 370141, Azerbaijan
[2] King Saud Univ, Coll Sci, Dept Math, POB 2455, Riyadh 11451, Saudi Arabia
[3] Sabanci Univ, Fac Engn & Nat Sci, TR-34956 Istanbul, Turkey
来源：
MEDITERRANEAN JOURNAL OF MATHEMATICS | 2022年 / 19卷 / 01期
关键词：
Reproducing kernel; reproducing kernel Hilbert space; Berezin transform; generalized Riccati operator equation; truncated operator; zero operator product; Englis algebra; TOEPLITZ-OPERATORS; BERGMAN SPACE; PRODUCTS; QUESTIONS; INVARIANT;
D O I：
10.1007/s00009-021-01926-y
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We give some applications of Berezin transforms and Engli ' s C*-algebras methods, namely we investigate the solution of generalized Riccati operator equation of the form XAX + Sigma(N)(i=1) BiXCi - D = 0, N >= 2 via Berezin transforms. Also, we study finite product of operators, including finite zero-product of Toeplitz operators on the Bergman Hilbert space L-a(2) (D) in terms of Berezin transforms. The same method is used for characterization of compact truncated operators on the reproducing kernel Hilbert space H = H(Omega)
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页数：16
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