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Research Interests:
Mathematical Physics
Complex Analysis
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YMN
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My interests include
- Bounded analytic
functions on the unit disk:
- Classical generalizations of Schwarz's Lemma
- Using the hyperbolic metric to understand Schwarz's
Lemma and its generalizations.
- Boundary versions of Schwarz's Lemma
- Iteration theory / complex dynamics
- 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
My current research projects include
- Using inner functions in boundary versions of
Schwarz's Lemma
- Viewing the works of P. Mercer (1997, 1999) and
others from within the hyperbolic metric
- Extending the works of D. Aharonov (1970) and Z.
Nehari (1970) regarding B.E. functions
A number of good references exist on the subject at
various levels:
-
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
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