The Research Seminar in Analysis in conjunction with the Colloquium at UMR meets again in G5 (Rolla Building) on Monday, Oct 23, 2000, 3:30 pm. All interested faculty and students are invited to attend.

Stefan Hilger (Katholische Universität Eichstätt) is lecturing on Discrete and continuous analysis via measure chains. One can generalize differential and integral calculus (for functions of one variable) by replacing the range of definition of the functions under consideration by an arbitrary measure chain (or time scale). This generalization will be presented in this talk, and an introduction to the calculus on measure chains is given. Whenever there are analogies in theories concerning discrete and continuous time scales, this calculus on measure chains is able to give a clear foundation for these analogies. It also provides tools for tracking down reasons for discrepancies arising in theorems for different time scales. Meanwhile this calculus has been applied in different areas of analysis, and in this talk several applications will be presented.