Linda Patton's Web Page: Research Interests
I am most interested in problems in operator theory and complex analysis, particularly Pick interpolation and composition operators. 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.
- "Numerical ranges of 4-by-4 nilpotent matrices:flat portions on the boundary", with E. Militzer, I.M. Spitkovsky, M.C. Tsai,
to appear in Operator Theory Adv. Appl.
- "Trace conditions for symmetry of the numerical range", with L. Deaett, R.H. Lafuente-Rodrigues, J. Marin Jr, K. Rasmussen, R.B. Johnson 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.