Mathematical Sciences: An Inverse Spectral Theory Problem for Bounded Domains in Two or More Dimensions

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Given a linear differential equation which may model a physical system one may seek the solutions based on a knowledge of the coefficients. The problem being addresses here is the inverse problem: Given some knowledge of the solutions try to determine the particular differential equation and hence the underlying physical system. The proposed research is directed to handle inverse problems in dimensions two or more based on the success achieved by the investigator with one-dimensional problems.