The Concept of a -Basis and an Application to the Fredholmness of a Banach-Valued Boundary Value Problem with Oblique Derivative
Siberian Mathematical Journal, vol.67, no.4, pp.745-755, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 67 Issue: 4
- Publication Date: 2026
- Doi Number: 10.1134/s0037446626040014
- Journal Name: Siberian Mathematical Journal
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET, Academic Search Ultimate (EBSCO), Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Page Numbers: pp.745-755
- Keywords: 517.957, Banach-valued harmonic function, Bochner space, Fredholmness, problem with oblique derivative
- Yıldız Technical University Affiliated: Yes
Abstract
We consider the concept of a -basis generated by the tensor product of Banach spaces.We introduce the concept of a -harmonic Banach-valued (-valued) function, where the space under consideration has an involution.Using the fact that the classical system of exponentials forms a -basis for the Bochner space of -valued functions with the UMD property, we define the Hardy class of -harmonic functions in the unit disk.We consider a boundary value problem with oblique derivative in this class and establish a criterion for the Fredholmness and, in particular, the solvability of this problem.Concrete examples are given.