Spectra of Compact Composition Operators
Copyright policy )Spectra of Compact Composition Operators
Let ϕ \phi be holomorphic and map the open unit disk into itself, and let C ϕ : f → f ∘ ϕ {C_\phi }:f \to f \circ \phi be the composition operator on H 2 {H^2} generated by ϕ \phi . If C ϕ {C_\phi } is a compact operator then ( 1 ) ϕ ( z 0 ) = z 0 (1)\phi ({z_0}) = {z_0} for some z 0 ϵ D {z_0} \epsilon D ; ( 2 ) σ ( C ϕ ) = { ϕ ′ ( z 0 ) n : n = 0 , 1 , 2 , … } ∪ { 0 } (2)\sigma ({C_\phi }) = \{ \phi ’{({z_0})^n}:n = 0,1,2, \ldots \} \cup \{ 0\} .
Banach spaces of continuous, differentiable or analytic functions, Spectrum, resolvent, \(H^p\)-classes, Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
Banach spaces of continuous, differentiable or analytic functions, Spectrum, resolvent, \(H^p\)-classes, Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).18 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!