Dynamics of Partial Differential Equations
Volume 2 (2005)
The inverse periodic spectral theory of the Euler-Bernoulli equation
Pages: 127 – 148
The Floquet (direct spectral) theory of the periodic Euler-Bernoulli equation has been developed by the author in , , and . A particular case of the inverse problem has been studied in . Here we focus on the inverse periodic spectral problem. A key ingredient is an extended version of Abel’s theorem for the existense of meromorphic functions on Riemann Surfaces. To avoid technicalities, we have assumed that the Floquet multiplier has finitely many branch points (in the Hill operator case this corresponds to the assumption that the spectrum has finitely many gaps).
Euler-Bernoulli (or beam) operator, Euler-Bernoulli equation for the vibrating beam, Hill’s operator, periodic coefficients, Floquet theory, spectrum, pseudospectrum, multipoint eigenvalue problem, inverse periodic spectral theory, Abel’s theorem
2010 Mathematics Subject Classification
Primary 34A55, 34B05. Secondary 34B10, 34B30, 34L40, 74B05.