Akademik Veri Yönetim Sistemi
TURAN-Fundamental Sciences Symposium (TURAN25), İstanbul, Türkiye, 23 - 25 Haziran 2025, ss.108, (Özet Bildiri)
In this work, we study the class hₚ(X) of X-valued harmonic functions defined on the unit disc, where X is a UMD space and 1 < p < ∞. The space is constructed using X-valued trigonometric series in the Bochner space Lₚ([−π, π); X), and the t-basis property of the exponential system is established. This structure provides the foundation for analysing boundary value problems, particularly the Laplace equation with directional derivative conditions. It is proved the Fredholmness of this problem. Additionally, harmonic and analytic X-valued function spaces are examined, including their relationship through generalized Cauchy-Riemann equations derived from a *-involution on X. A vector-valued version of Fatou’s theorem is also established. The study introduces derivative-based subspaces of hₚ(X), and the index of associated boundary value problems is computed.