“Zero-Sets of Functions in Bergman Spaces”








(Senior Project Presentation)



Abstract:  This is a Senior Project presentation

The Bergman space A^p consists of all holomorphic functions defined in the unit disc the p-th power of whose complex modulus is integrable with respect to the area measure.  We say {z_k} is an A^p zero-set if and only if there exists a function f in A^p such that f vanishes precisely on this set.  In this talk we will discuss properties of A^p zero-sets.  For this purpose the following three questions will be answered:  Do A^p zero sets vary with p?  In other words, does there exist an A^q zero-set that is not an A^p zero-set for two positive real numbers p and q?  Is the union of two A^p zero-sets an A^p zero-set?  Must every subset of an A^p zero-set be an A^p zero set?  I will mainly follow Charles Horowitz's 1974 work in which all three questions are answered.



Date:  Tuesday, December  23, 2014

Time: 15:40

Place: Mathematics Seminar Room, SA-141



Tea and cookies will be served before the seminar.