Faculty Juan Jorge Schäffer, Professor
Dr.sc.techn., Swiss Federal Institute of Technology
Dr.phil., University of Zurich
E-mail: js6n@andrew.cmu.edu
Office: Wean Hall 6206
Phone: 412-268-2549

Research:

Functional analysis is an essential component of most of my recent research. One main area is the theory of ordinary and functional differential equations. Continuing the work developed in the monograph by J.L. Massera and myself, Linear Differential Equations and Function Spaces (Academic Press, 1966), I have, often in collaboration with C.V. Coffman (CMU), obtained results on the conditional stability and structure of linear functional differential equations with bounded and unbounded delays, under very general "natural Caratheodory conditions."

Another of my areas of interest is the geometry of normed spaces. My earlier work on certain metric parameters of the unit spheres is described in the monograph Geometry of Spheres in Normed Spaces (M. Dekker, 1976), and I'm continuing research on the isometric and isomorphic properties of these parameters. I'm also currently pursuing research, partly in collaboration with W. Noll (CMU), on geometry and analysis in linear cones, with applications to continuum mechanics.

Selected Publications:

• Garay, B.M. and Schäffer, J.J. (1986), "More on Uniqueness without Continuous Dependence in Infinite Dimension," J. Differential Equations 64: 48–50.
• Schäffer, J.J. (1984), "Exponential Dichotomies for Linear Differential Equations with Delays: Periodic and Autonomous Equations," Ann. Mat. Pura Appl. (4) 138: 105–149.
• Schäffer, J.J. (1981), "Natural Metrics on Faceless Cones," Ann. Mat. Pura Appl., (4) 127: 173–185.
• Schäffer, J.J. (1980), "Girth, Super-Reflexivity, and Isomorphic Classification of Normed Spaces and Subspaces," Bull. Acad. Polon. Sci. Ser. Sci. Math. 28: 573–584.