Gesammelte Werke, Band IV: Analysis, Algebra und Zahlentheorie
This is the first of eight planned volumes devoted to the work of F. Hausdorff (including physics and his literary work). The pattern is the same throughout: Hausdorff’s writing (published or unpublished) is followed by a commentary by a current expert in the area. The part devoted to analysis occupies about 80% of the book, and consists of 13 of Hausdorff’s published research papers from 1914-31 and 19 items (from 1914-42) devoted to analysis and found in his inheritance. We find here classical papers on measure theory and the moment problem; among unpublished papers we notice the introduction of the long line in 1915, results on trigonometric series, extensions of measures, orthogonal polynomial functions, and functions with special properties. In a letter to L. Bieberbach, Hausdorff suggested a simplification of one of Bieberbach’s results concerning holomorphic functions. The second part devoted to algebra contains three published papers and one unpublished paper. The number theory part consists of two published papers. The book concludes with an extensive author index and two subject indexes, German and English.