• Corpus ID: 218530592

Can one Hear the Shape of a Drum?

@inproceedings{Verhoeven2015CanOH,
  title={Can one Hear the Shape of a Drum?},
  author={Luuk S. Verhoeven and Walter D. van Suijlekom},
  year={2015}
}
waltervansuijlekom.nl
200 Citations
Highly Influential Citations
18
Background Citations
137
Methods Citations
12
Results Citations
1

200 Citations

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Explorations of Infinitesimal Inverse Spectral Geometry

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Transient response functions for graph structure addressable memory

  • W. Gong
  • Computer Science
    52nd IEEE Conference on Decision and Control
  • 2013
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References

SHOWING 1-10 OF 16 REFERENCES

Eigenvalues of the Laplacian for rectilinear regions

  • H. Gottlieb
  • Mathematics
    The Journal of the Australian Mathematical Society. Series B. Applied Mathematics
  • 1988
Abstract From a knowledge of the eigenvalue spectrum of the Laplacian on a domain, one may extract information on the geometry and boundary conditions by analysing the asymptotic expansion of a…

The spectrum of positive elliptic operators and periodic bicharacteristics

Let X be a compact boundaryless C ∞ manifold and let P be a positive elliptic self-adjoint pseudodifferential operator of order m>0 on X. For technical reasons we will assume that P operates on…

Heat equation for a region in R2 with a polygonal boundary

Soit D un ensemble connexe ouvert borne dans R 2 a frontiere ∂D. Soit Δ le laplacien de Dirichlet pour D et on definit pour t positif Z(+)=trace (exp iΔ). On etudie le comportement de Z(t) dans le…

Contribution of periodic diffractive geodesics

The Poisson Summation Formula for Manifolds with Boundary

Introduction to Fourier Analysis on Euclidean Spaces.

The authors present a unified treatment of basic topics that arise in Fourier analysis. Their intention is to illustrate the role played by the structure of Euclidean spaces, particularly the action…

Can one hear the shape of a drum

Fourier Analysis: An Introduction

This book discusses Fourier Analysis, Dirichlet's Theorem, and some Applications of Fourier Series 100 with a focus on the Fourier Transform.

On the inverse spectral problem for polygonal domains

Eigenvalues and Eigenfunctions of the Laplacian 24 2 The Eigenvalue Problem 2 . 1 The eigenvalue equation

The problem of determining the eigenvalues and eigenvectors for linear operators acting on finite dimensional vector spaces is a problem known to every student of linear algebra. This problem has a…