## Department / Division

- Faculty-Mathematics

## Title

- Professor Emeritus

## Contact

Email: neumann@math.msstate.edu

**Research interests:** Functional analysis, operator theory, local spectral theory of operators on Banach spaces and its connections to Banach algebras, harmonic analysis, and automatic continuity, convex analysis with applications to network flows and mathematical economics.

**Research Description**

Having done research in mathematics for more than 40 years, I continue to be interested in a variety of fields. One of my research areas is local spectral theory which allows to make progress on the spectral theory of operators on Banach spaces far beyond the realm of Hilbert spaces. Here the tools are from complex analysis, sheaf theory, and the theory of topological vector spaces.

I am also interested in optimization problems from classical applied mathematics and mathematical physics. In particular, I employ methods of real analysis to study the optimization of projectile motion under the notoriously challenging condition of air resistance quadratic in speed where no explicit solution formulas for the underlying system of differential equations are known.

More recently, I have also become involved in the real analysis in reverse program with emphasis on convergence tests for infinite series in arbitrary ordered fields and the intimate connections to the notions of Cauchy and Dedekind completeness in such fields.

**Degree:** Ph.D. in Mathematics, 1974,

Department of Mathematics, University of Saarbrucken, Germany

**Curriculum Vitae: **Dr. Neumann's CV