New Titles  |  FAQ  |  Keep Informed  |  Review Cart  |  Contact Us Quick Search (Advanced Search ) Browse by Subject General Interest Logic & Foundations Number Theory Algebra & Algebraic Geometry Discrete Math & Combinatorics Analysis Differential Equations Geometry & Topology Probability & Statistics Applications Mathematical Physics Math Education

Inverse Nodal Problems: Finding the Potential from Nodal Lines
Ole H. Hald, University of California, Berkeley, CA, and Joyce R. McLaughlin, Rensselaer Polytechnic Institute, Troy, NY
 SEARCH THIS BOOK:
Memoirs of the American Mathematical Society
1996; 148 pp; softcover
Volume: 119
ISBN-10: 0-8218-0486-3
ISBN-13: 978-0-8218-0486-5
List Price: US$45 Individual Members: US$27
Institutional Members: US\$36
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.

Features:

• The formulas that solve the inverse problem are very simple and easy to state.
• Nodal Line Patterns-Chaldni Patterns-are shown to be a rich source of data for the inverse problem.
• The data in this book is used to establish a simple formula that is the solution of an inverse problem.

Undergraduates studying PDEs, graduate students, and research mathematicians interested in analysis with emphasis on inverse problems.

• Eigenvalues for $$- \Delta + q$$
• Eigenfunctions for $$- \Delta + q$$
• The case $$f_R q\neq 0$$