On the eigenvalue ratio for vibrating strings
Author:
MinJei Huang
Journal:
Proc. Amer. Math. Soc. 127 (1999), 18051813
MSC (1991):
Primary 34L15
Published electronically:
February 17, 1999
MathSciNet review:
1621941
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Abstract: For vibrating strings with concave densities or symmetric singlebarrier densities, the ratio of the first two eigenvalues is minimized when the density is constant; while, for vibrating strings with symmetric singlewell densities, the ratio is maximized when the density is constant.
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 R. D. Gentry and D. O. Banks, Bounds for functions of eigenvalues of vibrating systems, J. Math. Anal. Appl. 51 (1975), 100128. MR 51:8528
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 J. B. Keller, The minimum ratio of two eigenvalues, SIAM J. Appl. Math. 31 (1976), 485491. MR 54:10737
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Additional Information
MinJei Huang
Affiliation:
Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan 30043
Email:
mjhuang@math.nthu.edu.tw
DOI:
http://dx.doi.org/10.1090/S0002993999050157
PII:
S 00029939(99)050157
Keywords:
Eigenvalue ratio,
eigenfunction,
concave density,
symmetric singlewell density
Received by editor(s):
September 19, 1997
Published electronically:
February 17, 1999
Communicated by:
Hal L. Smith
Article copyright:
© Copyright 1999
American Mathematical Society
