Tangential interpolation problems for a class of automorphic matrix-functions

Bekker, Miron B.; Nudel’man, A. A.

doi:10.1016/j.laa.2004.10.007

Cited by 2 publications

(2 citation statements)

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“…For the readers convenience, we mention here briefly some of these connections. One motivation comes from earlier work [1] on two-sided, and tangential, interpolation for matrix functions; see also references [2] through [5], and [14]. We make additional connections also to to interpolation in de Branges-Rovnyak spaces [13], to wavelet filters, see e.g., [17], and to iterated function systems, see [18] by Courtney, Muhly, and Schmidt, and [28] by Rochberg, to Hardy classes [29,30] and to classical harmonic analysis; see e.g., [32,33,34,35].…”

Section: Introductionmentioning

confidence: 99%

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Representation Formulas for Hardy Space Functions Through the Cuntz Relations and New Interpolation Problems

Alpay

Jørgensen

Lewkowicz

et al. 2012

Multiscale Signal Analysis and Modeling

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We introduce connections between the Cuntz relations and the Hardy space H 2 of the open unit disk D. We then use them to solve a new kind of multipoint interpolation problem in H 2 , where for instance, only a linear combination of the values of a function at given points is preassigned, rather than the values at the points themselves.1991 Mathematics Subject Classification. 42C40, 47A57, 93B28. Key words and phrases. Cuntz relations, Leech's theorem, Schur analysis. D. Alpay thanks the Earl Katz family for endowing the chair which supported his research. The work was done in part while the second named author visited Department of Mathematics, Ben Gurion University of the Negev, supported by a BGU distinguished visiting scientist program. Support and hospitality is much appreciated. We acknowledge discussions with colleagues there, and in the US, Dorin Dutkay, Myung-Sin Song, and Erin Pearse.

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Section: Introductionmentioning

confidence: 99%

“…Unfortunately this method does not extend to the case M > 2. For a related interpolation problem (for Nevanlinna functions), see also [14], where the n-th composition of the map ϕ is equal to the identity map: ϕ •n (z) = z.…”

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confidence: 99%