Abstract
Let D be a simply connected bounded domain in the complex plane C1 with rectifiable boundary ∂D. For the functions ƒ from the Hardy class H1(D) the Cauchy formula (see [134, p. 205])
is valid. Let us consider on the boundary ∂D a measurable set M of positive Lebesgue measure. The problem is to reconstruct f(z) in D from its values not on the whole boundary ∂D as in (1.1) but on M ⊂ ∂D only. Applying a simple, but very fruitful idea of Carleman we construct a “quenching” function, enabling us to eliminate in (1.1) integration over ∂D\ M.
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© 1993 Springer Science+Business Media Dordrecht
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Aizenberg, L. (1993). One-Dimensional Carleman Formulas. In: Carleman’s Formulas in Complex Analysis. Mathematics and Its Applications, vol 244. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1596-4_1
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DOI: https://doi.org/10.1007/978-94-011-1596-4_1
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4695-4
Online ISBN: 978-94-011-1596-4
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