# Research Interests

I am most interested in problems in operator theory and complex analysis, particularly composition operators, numerical ranges, and Pick interpolation. Cal Poly students who are interested in a senior project involving linear algebra and/or complex analysis should contact me by email or during office hours.

## Publications

- "Trace Conditions for Symmetry of the Numerical Range", with L. Deaett, R.H. Lafuente-Rodrigues, J. Marin Jr, E.H. Martin, K. Rasmussen, R.B. Johhnson Yates,
*Electronic Journal of Linear Algebra*,**26**, (2013), 591-603.

- "Some block Toeplitz composition operators",
*J. Math. Anal. Appl.***Volume 400 (2)**(2013), 363-376.

- "Numerical ranges of cube roots of the identity", with T.R. Harris, M. Mazzella, D. Renfrew, I.M. Spitkovsky,
*Linear Algebra and its Applications*,**435**, (2011), 2639-2657.

- "Norm inequalities for composition operators on Hardy and weighted Bergman spaces", with Christopher Hammond,
*Operator Theory Adv. Appl.,***202**, Birkhauser Basel (2010), 265-272. .

- "Approximating composition operator norms on the Dirichlet space", with Marian Robbins,
*J. Math. Anal. Appl.*,**Volume 339 (2)**(2008), 1374-1385.

- "On multivariable Fejér inequalities", with Mihai Putinar,
*Acta Sci Math. (Szeged)*,**72**(2006), 129-134.

- "Composition operators that are m-sometries", with Marian Robbins,
*Houston Journal of Mathematics*,**31**, no. 1, (2005), 255-266.

- "Commutation relations for Toeplitz and Hankel matrices", with Caixing Gu,
*SIAM J. Matrix Anal. Appl.*,**24**, no. 3, (2003), 728-746.

- "Caratheodory-Fejér interpolation on polydisks", with Jörg Eschmeier and Mihai Putinar,
*Math Research Letters*,**7**, (2000), 25-34.

- "Some solutions of the matrix equation for Nevanlinna-Pick interpolation",
*Linear Algebra and its Applications*,**254**, (1997), 467-484.

- "Interpolation of Nevanlinna-Pick type on the boundary of the bidisc",
*Complex Variables: Theory and Application*,**24**, no. 1-2, (1994), 107-120.