Research Seminar in Analysis in conjunction with the Colloquium at UMR
meets again in G5 (Rolla Building)
on Wednesday, May 9, 2001, 3:30 pm.
All interested faculty and students are invited to attend.
Cauchy and Connection Problems.
From the Identity Theorem in complex analysis, it turns out that for any analytic function, there exists a sequence of complex numbers which completely determines it, including all singular behavior and its complete analytic continuation. Such a sequence can be considered as a "genetic code" for the function and the theme for this talk will concern how the singular behavior is encoded in the sequence and how possibly to decode this information. While for general analytic functions this is too ambitious a goal, for functions which are solutions of meromorphic differential equations, recent results show that there indeed do exist codes for which the program can be realized. Three types of examples of codes will be considered.