Gian-Carlo Rota on Analysis and Probability: Selected Papers and Commentaries

Description

Gian-Carlo Rota was born in Vigevano, Italy, in 1932. He died in Cambridge, Mas­sachusetts, in 1999. He had several careers, most notably as a mathematician, but also as a philosopher and a consultant to the United States government. His mathe­matical career was equally varied. His early mathematical studies were at Princeton (1950 to 1953) and Yale (1953 to 1956). In 1956, he completed his doctoral thesis under the direction of Jacob T. Schwartz. This thesis was published as the pa­per "Extension theory of differential operators I", the first paper reprinted in this volume. Rota's early work was in analysis, more specifically, in operator theory, differ­ential equations, ergodic theory, and probability theory. In the 1960's, Rota was motivated by problems in fluctuation theory to study some operator identities of Glen Baxter (see [7]). Together with other problems in probability theory, this led Rota to study combinatorics. His series of papers, "On the foundations of combi­natorial theory", led to a fundamental re-evaluation of the subject. Later, in the 1990's, Rota returned to some of the problems in analysis and probability theory which motivated his work in combinatorics. This was his intention all along, and his early death robbed mathematics of his unique perspective on linkages between the discrete and the continuous. Glimpses of his new research programs can be found in [2,3,6,9,10]. Introduction and Reminiscences Chapter 1. Differential Operators Chapter 2. Theory of Linear Operators Chapter 3. Reynolds Operators Chapter 4. Ergodic Theory Chapter 5. Inequalities Chapter 6. Geometric Probability and Profinite Combinatorics Chapter 7. Probability Theory.