Inverse Nodal Problems: Finding the Potential from Nodal Lines (Memoirs of the American Mathematical Society v. 119)

Inverse Nodal Problems: Finding the Potential from Nodal Lines (Memoirs of the American Mathematical Society v. 119)

By: Joyce R. McLaughlin (author), Ole H. Hald (author)Paperback

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Description

Can you hear the shape of a drum? 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 Schrodinger 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. 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.

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Contents

Introduction Separation of eigenvalues for the Laplacian Eigenvalues for the finite dimensional problem Eigenfunctions for the finite dimensional problem Eigenvalues for $- \Delta + q$ Eigenfunctions for $- \Delta + q$ The inverse nodal problem The case $f R q\neq 0$ Acknowledgment References Appendices.

Product Details

  • publication date: 15/02/1996
  • ISBN13: 9780821804865
  • Format: Paperback
  • Number Of Pages: 148
  • ID: 9780821804865
  • weight: 292
  • ISBN10: 0821804863

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