ABSTRACT
Giuseppe Vitali’s life and scientific achievements are closely connected with Bologna and its University. This chapter focuses on Vitali’s papers on complex analysis. Vitali’s papers have as a premise a honest knowledge of a part of the classical treatise by Appell – Goursat on algebraic functions and the older treatises of Neumann and Briot on abelian integrals and abelian functions. An abstract logical appraisal could suggest a natural continuous evolution from Dini’s work to Vitali’s work through Ascoli, Arzela and Volterra’s writings on real function theory. Vitali possessed a detailed knowledge of Arzela’s work and it influenced some important papers of Vitali, namely the papers on series or sequences of holomorphic functions. However, the influence of Arzela’s work on Vitali must not be overestimated because Vitali’s contribution to analysis was conceptually a novelty and truly original.
