Robert F. Allen, Ph.D.

Primary interests

Operator theory, weighted composition operators, Bloch functions, real/complex/harmonic analysis, pattern formation in PDEs, mathematical biology.

Other interests

Lie algebras, operator algebras, category theory, reverse mathematics, formal methods in software engineering.

• Bifurcations in an epidemiology model: Surviving an outbreak of zombiism, co-authored with C. Jens and T. Wendt, in preparation.
• Multiplication operators on the iterated logarithmic Lipschitz space of a tree, co-authored with F. Colonna and G. R. Easley, submitted to the Mediterranean Journal of Mathematics.
• Multiplication operators between Lipschitz-type spaces of a tree, co-authored with F. Colonna and G. R. Easley. submitted to the International Journal of Mathematics and Mathematical Sciences.
• Multiplication operators on the weighted Lipschitz space of a tree, co-authored with F. Colonna and G. R. Easley. J. Operator Theory, accepted.
• Weighted composition operators between H^∞ and the Bloch space of a bounded homogeneous domain, co-authored with F. Colonna. Integr. Equ. Oper. Theory 66 (2010), 21-44..
• Weighted composition operators on the Bloch space of a bounded homogeneous domain, co-authored with F. Colonna. Operator Theory: Advances and Applications, Vol. 202, 11-37..
• Multiplication operators on the Bloch space of a bounded homogeneous domain, co-authored with F. Colonna. Comp. Methods Funct. Theory 9 no. 2 (2009), 679-693.
• On the isometric composition operators on the Bloch space in Cⁿ, co-authored with F. Colonna. J. Math. Anal. Appl. 355 no. 2 (2009), 675-688
• Isometries and spectra of multiplication operators on the Bloch space, co-authored with F. Colonna. Bull. Aust. Math. Soc. 79 no. 1 (2009), pp. 147-160.

• A class of operator with symbol on the Bloch space of a bounded homogeneous domain. Ph.D. dissertation, George Mason University (2009).
• Turing instabilities and spatial pattern formation in one-dimension. Undergraduate honors thesis, George Mason University (2003).
• The design and implementation of the C-- programming language. Undergraduate thesis, University of Virginia (1994).