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ABSTRACT We study the Cauchy representation formula for analytic functions on the unit disc whose pointwise boundary value function is distributionally integrable. We prove that the formula holds when the… Click to show full abstract
ABSTRACT We study the Cauchy representation formula for analytic functions on the unit disc whose pointwise boundary value function is distributionally integrable. We prove that the formula holds when the distributional boundary values exist, and give examples that show that it may not be true when that is not the case. We also prove a maximum principle for pointwise boundary values valid for functions with distributional boundary values.
Keywords:
cauchy integral;
integral formula;
formula;
boundary values;
formula distributional;
distributional integration
Journal Title: Complex Variables and Elliptic Equations
Year Published: 2018
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Journal Title: Complex Variables and Elliptic Equations
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!