2017/10/01 by Vladimir Ryazanov, Ryazanov, Vladimir
Computer Science · Mathematics · #30C62 #31A05 #31A20 #31A25 #31B25 (Primary) 30E25 #31C05 #34M50 #35F45 #35Q15 (Secondary) #Advanced Mathematical Modeling in Engineering #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.1710.00323
openalex publication_date 2017/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is established that if a harmonic function u on the unit disk \mathbb D in \mathbb C has angular limits on a measurable set E of the unit circle ∂\mathbb D, then its conjugate harmonic function v in \mathbb D also has angular limits a.e. on E and both boundary functions are finite a.e. and measurable on E. The result is extended to arbitrary Jordan domains with rectifiable boundaries in terms of angular limits and of the natural parameter.