Harmonic Analysis and Several Complex Variables Seminar - Valentin Kunz

Valentin Kunz
The Ohio State University

Title
Several Complex Variables and the Quarter-Plane Problem: An Overview

Abstract
The 'quarter-plane problem' refers to the boundary value problem which models the interaction of a monochromatic plane-wave, e.g., an acoustic pressure field, with the tip of an infinitely thin corner in three spatial dimensions, e.g., the tip of a turbofan blade. In this talk, we will outline how the theory of several complex variables can help us gain a better understanding of such physical phenomena. We are particularly interested in finding an asymptotic formula for the field observed at a great distance from the quarter-plane, which, in turn, requires knowledge of the singularity structure of some two-complex-variable spectral functions.

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