From its Origins to Recent Results for Weakly Pseudoconvex Domains - Speaker: Prof. R. Michael Range (State University of New York at Albany) -
Abstract: The familiar classical Cauchy kernel has numerous important applications, so it is a central topic in multidimensional complex analysis to study
correspond- ing higher dimensional kernels and applications. We shall begin this series of lectures with a quick review of such well known generalizations and results.
We will then cover in detail a recent kernel construction that is valid on arbitrary smoothly bounded weaklν (that is, not necessarily strictlν ) pseudoconvex do- mains and that opens the door to significant applications. In that generality it is not possible
to construct explicit kernels that are holomorphic in the parameter. Instead, the goal is to preserve some estimates that reflect the complex
geom- etry of the boundary and the special role of differentiation with respect to the complex conjugate variables. We will discuss some basic properties of the new kernel and use them to obtain some pointwise a-priori
estimates for (0, q) forms that are the analogue
of the classical basic estimate on pseudoconvex domains in the L2 theory of the complex Neumann problem. - Place: GAIA Seminar Room (#106, Math Science bldg.) - Date I. 8:00 - 10:00 P.M. on Monday, April 13, 2015 II. 4:00 - 6:00 P.M. on Tuesday, April 14, 2015 Ⅲ. 8:00 - 10:00 P.M. on Monday, April 20, 2015 Ⅳ. 4:00 - 6:00 P.M. on Tuesday, April 21, 2015
For further information, please contact: Kang-Tae kim(kimkt@postech.ac.kr) |
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