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On determinant expansions for Hankel operators
Gordon Blower1; Yang Chen2
Source PublicationarXiv

Let w be a semiclassical weight which is generic in Magnus’s sense, and (pn)∞ n=0 the corresponding sequence of orthogonal polynomials. The paper expresses the Christoffel–Darboux kernel as a sum of products of Hankel integral operators. For ψ ∈ L∞(iR), let W(ψ) be the Wiener-Hopf operator with symbol ψ. The paper gives sufficient conditions on ψ such that 1/ detW(ψ)W(ψ −1 ) = det(I − Γφ1 Γφ2 ) where Γφ1 and Γφ2 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 nFm. These results extend those of Basor and Chen [2], who obtained 4F3 likewise. The paper includes examples where the Wiener–Hopf factors are found explicitly.

KeywordOrthogonal Polynomials Special Functions Wiener-hopf Linear Systems
Fulltext Access
Document TypeJournal article
CollectionFaculty of Science and Technology
Corresponding AuthorGordon Blower
Affiliation1.Department of Mathematics and Statistics, Lancaster University, Lancaster, LA14YF, United Kingdom
2.Department of Mathematics, University of Macau, Avenida da Universidade, Taipa, Macau, China
Recommended Citation
GB/T 7714
Gordon Blower,Yang Chen. On determinant expansions for Hankel operators[J]. arXiv,2019.
APA Gordon Blower,&Yang Chen.(2019).On determinant expansions for Hankel operators.arXiv.
MLA Gordon Blower,et al."On determinant expansions for Hankel operators".arXiv (2019).
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