My interests include

• Bounded analytic functions on the unit disk:
• Classical generalizations of Schwarz's Lemma
• Schwarz-type lemmas for the hyperbolic derivative and it's higher-order relatives.
• Extending current boundary versions of Schwarz's Lemma
• Bieberbach-Eilenberg functions:
• Geometric properties of the function set
• Extensions of Schwarz-like inequalities to B.E. functions
• Special Analytic Functions:
• Laplace transforms (of positive functions) - analyticity and zeros
• Continued fractions with analytic entries

1. Constructing counterexamples to limit generalizations of Schwarz's Lemma
2. Analyzing generalized Schur coefficients within the hyperbolic metric

• Introductory Texts
  • Complex Variables with Applications by R.V. Churchill and Brown - An easy perennial favorite used at Rutgers and at Drew University.
  • Basic Complex Analysis by J.E. Marsden - A slightly bigger and more comprehensive text used at Wayne State University. I personally prefer its treatment of notions such as uniform convergence and the Cauchy Integral Formula.
  • An Introduction to Classical Complex Analysis by R.B. Burckel - a great text for those really looking for an extensive list of interesting exercises and an exhaustive bibliography.
• Specialized Texts
  • Banach Spaces of Analytic Functions by Kenneth Hoffman- This book is indispensable to me and a great Dover value for only $7.95.
  • Iteration Theory of Holomorphic Maps on Taut Manifolds by Marco Abate - Helps you understand analytic functions from the geometric and dynamical viewpoints both in one and several complex variables
  • Geometric Function Theory: Explorations in Complex Analysis by Steven Krantz - Currently reviewing the text. Pretty good so far with a good introduction to the Bergmann Kernel, Schwarz's Lemma
  • The Cauchy Transform by Joseph A. Cima, Alec L. Matheson, William T. Ross - Currently reading the text. It appears to read quite well. I'm interested in its treatment of Aleksandrov-Clark measures.