Nagel DMS-9501041 Nagel will study a variety of problems in complex and harmonic analysis. The first will be to study certain aspects of function theory on non-pseudoconvex domains of finite type in complex 2-space. The second will be to study certain model generic CR submanifolds of CR dimension 1 in higher dimensional spaces. The final problem is to study certain special cases of domains of finite type in complex n-space where n is greater than two. All three involve the interplay of complex and harmonic analysis, as well as aspects of linear pde's. Classical function theory has introduced geometric techniques which have proved to have far wider applicability than first imagined. The subject exploits the interplay between geometric interpretation with powerful analytic techniques to yield some of the most complete mathematical results in the field of analysis.
