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Trace Formulas for Powers of a Sturm-Liouville Operator

Published online by Cambridge University Press:  20 November 2018

Richard C. Gilbert  and
Vernon A. Kramer
Richard C. Gilbert
Affiliation:
University of California at Riverside and Mathematics Research Center, University of Wisconsin
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Let H0 be the mth power (m a positive integer) of the self-adjoint operator defined in the Hilbert space L2(0, π) by the differential operator — (d2/dx2) and the boundary conditions u(0) = u(π) = 0. The eigenvalues of H0 are μn = n2m and the corresponding eigenfunctions are ϕn = (2/π)1/2 sin nx, n = 1 , 2 , . . ..

Let p be a (2m — 2)-times continuously differentiate real valued function defined over the interval [0, π] satisfying the conditions p(j)(0) = p(j)(π) = 0 for j odd and less than 2m — 4.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 412 - 422
Copyright
Copyright © Canadian Mathematical Society 1964

References

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