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- W8777788 abstract "In this paper some questions related to Hankel operators associated with Markov functions are considered. Let G be a bounded multiply connected domain with a boundary Γ consisting of closed analytic Jordan curves. We assume that G is symmetric with respect to the real axis. Let µ be a positive Borel measure with the support supp µ = E ⊂ R, E ⊂ G. We investigate a connection between the Hankel operator A f constructed from the Markov function $$ fleft( z right) = frac{1}{{2pi i}}int_{E} {frac{{dmu left( x right)}}{{z - x}}} $$ and the embedding operator J: E 2 (G) → L 2 (μ,E), where E 2 (G) is the Smirnov class of functions analytic on G. Moreover, in the case when G is the open unit disk we state results characterizing the rate of decrease of the sequence of singular numbers of the Hankel operator A f constructed from the Markov function with the measure μ satisfying the Szegö condition: supp μ = [a, b] ⊂ (-1,1) and $$ int_a^b {frac{{log left( {dmu /dx} right)}}{{sqrt {left( {x - a} right)left( {b - x} right)} }}dx > - infty .} $$" @default.
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- W8777788 date "2001-01-01" @default.
- W8777788 modified "2023-10-18" @default.
- W8777788 title "On Hankel Operators Associated with Markov Functions" @default.
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- W8777788 doi "https://doi.org/10.1007/978-3-0348-8362-7_3" @default.
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