Тип публикации: доклад, тезисы доклада, статья из сборника материалов конференций
Конференция: 9th International School-Seminar on Nonlinear Analysis and Extremal Problems (NLA-2026); Irkutsk; Irkutsk
Год издания: 2026
Ключевые слова: Banach space with reproducing kernel, Hardy space, duality theorems, sparse minimizing
Аннотация: We consider the Hardy space ℋ(), 1 < < +∞, of holomorphic functions on bounded simply connected plane domain as a Banach space with reproducing kernel. For = 2 the reproducing kernels of the Hilbert spaces ℋ2() were identified for a number of domains of special types (a disc, a half plane and so on). However, for general plane dПоказать полностьюomain there are no simple formulae for the kernels. Using deep connection of the natural pairing between the Lebesgue spaces () and (), 1/+1/ = 1, with the classical Grothendieck-Köthe-Silva duality, we identify the reproducing kernel of the space ℋ() as the Cauchy kernel. As an application of this fact we investigate probem of the so-called sparse minimizing of proper convex coercive lower semi-continuous functionals on the Hardy spaces ℋ() related to finite-dimensional space of data.
Журнал: Proceedings of the 9th International School-Seminar on Nonlinear Analysis and Extremal Problems (NLA-2026)
Номера страниц: 29
Место издания: Irkutsk