Memories about
Solomon Marcus


Much of the early part of my career was influenced by Solomon Marcus, both through his work and through correspondence. Almost fifty five years ago, I was working on a project involving generalisations of convex functions of a real variable. I realised that, in order to complete this project, I needed to understand the fine structure of ordinary derivatives of real functions defined on the line. In searching the literature, I discovered a number of useful papers, many of which were written by Solomon Marcus. I wrote him, and he responded with a long letter containing useful insights, many suggestions, and a number of important references. Over the next few years, our correspondence continued, and I appreciated the encouragement I received from him. The result was that I spent most of my career working in the area of functions of a real variable, his area of interest at the time. (I never returned to the original convexity project.)
      Over the years, I noticed that Solomon Marcus had many imaginative ideas that he developed and he posed interesting problems for others to attack. His writings were always well written, well motivated, and pleasant to read. Even his short papers prompted others to continue his work. For example, he introduced the notions of stationary sets and determining sets for a class of functions. He wrote several papers on the subject, in which he characterised such sets for a number of classes of functions related to differentiation theory. A number of authors continued his work by characterising such sets for other classes of functions. His correspondence also contained a number of problems that became of interest to other mathematicians. In a letter to me, many years ago, he noted that the class of derivatives is not closed under multiplication. He made a number of insightful comments which led to the problem of characterising the algebra generated by the derivatives. This problem led to many papers, some of which were quite deep, by many authors. The problem was finally solved by David Preiss who obtained the remarkable result that the algebra in question is just the algebra of functions in the first class of Baire. […]

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