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On Determinant Expansions for Hankel Operators
Blower,Gordon1; Chen,Yang2
Source PublicationConcrete Operators

Let w be a semiclassical weight that is generic in Magnus's sense, and (pn)n=0∞ ({p-n})-{n = 0}^\infty the corresponding sequence of orthogonal polynomials. We express the Christoffel-Darboux kernel as a sum of products of Hankel integral operators. For ψ ∈ L (iâ.,?), let W(ψ) be the Wiener-Hopf operator with symbol ψ. We give sufficient conditions on ψ such that 1/det W(ψ) W(ψ) = det(I-Γ Γ ) where Γ and Γ are Hankel operators that are Hilbert-Schmidt. For certain, ψ Barnes's integral leads to an expansion of this determinant in terms of the generalised hypergeometric F. These results extend those of Basor and Chen [2], who obtained F likewise. We include examples where the Wiener-Hopf factors are found explicitly.

KeywordLinear Systems Orthogonal Polynomials Special Functions Wiener-hopf
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Indexed ByESCI
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000513762300002
Scopus ID2-s2.0-85081992689
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Cited Times [WOS]:1   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionUniversity of Macau
Corresponding AuthorBlower,Gordon
Affiliation1.Department of Mathematics and Statistics,Lancaster University,Lancaster,LA14YF,United Kingdom
2.Department of Mathematics,University of Macau,Avenida da Universidade,Taipa,Macao
Recommended Citation
GB/T 7714
Blower,Gordon,Chen,Yang. On Determinant Expansions for Hankel Operators[J]. Concrete Operators,2020,7(1):13-44.
APA Blower,Gordon,&Chen,Yang.(2020).On Determinant Expansions for Hankel Operators.Concrete Operators,7(1),13-44.
MLA Blower,Gordon,et al."On Determinant Expansions for Hankel Operators".Concrete Operators 7.1(2020):13-44.
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