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Memoirs of the American Mathematical Society
1996; 148 pp; softcover
List Price: US$48
Individual Members: US$28.80
Institutional Members: US$38.40
Order Code: MEMO/119/572
Can you hear the shape of a drum? No. In this book, the authors ask, "Can you see the force on a drum?"
Hald and McLaughlin prove that for almost all rectangles the potential in a Schrödinger equation is uniquely determined (up to an additive constant) by a subset of the nodal lines. They derive asymptotic expansions for a rich set of eigenvalues and eigenfunctions. Using only the nodal line positions, they establish an approximate formula for the potential and give error bounds.
The theory is appropriate for a graduate topics course in analysis with emphasis on inverse problems.
Undergraduates studying PDEs, graduate students, and research mathematicians interested in analysis with emphasis on inverse problems.
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