Abstract
AbstractWe define and study Toeplitz operators on the Fréchet space of all holomorphic functions on finitely connected domains in the Riemann sphere. We completely characterize Fredholm, semi-Fredholm and invertible operators belonging to this class. As a result, we obtain a characterization of these classes of operators in the unit disk case. As a motivation we formulate and analyze the Riemann–Hilbert problem in the space of all holomorphic functions on the domains which we consider.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Geometry and Topology,Algebra and Number Theory,Analysis
Reference50 articles.
1. Abrahamse, M.B.: Toeplitz operators in multiply connected regions. Am. J. Math. 96, 261–297 (1974)
2. Albanese, A.A., Bonet, J., Ricker, W.J.: Operators on the Fréchet sequence spaces $$ces(p+)$$, $$1\le p<\infty $$. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 113(2), 1533–1556 (2019)
3. Albanese, A.A., Bonet, J., Ricker, W.J.: Linear operators on the (LB)-sequence spaces $$ces(p-)$$, $$1
4. Albanese, A.A., Bonet, J., Ricker, W.J.: The Cesáro operator in weighted $$l^{1}$$ spaces. Math. Nachr. 291(7), 1015–1048 (2018)
5. Albanese, A.A., Bonet, J., Ricker, W.J.: The Cesáro operator on duals of power series spaces of infinite type. J. Oper. Theory 79(2), 373–402 (2018)
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