zbMATH — the first resource for mathematics

Some properties of lacunary series in the study of elastic vibrations. (Quelques propriétés des séries lacunaires utiles dans l’étude des vibrations élastiques.) (French) Zbl 0805.35070
Brezis, H. (ed.) et al., Nonlinear partial differential equations and their applications. Collège de France Seminar, volume XII. Lectures held at the weekly seminar on applied mathematics, Paris, France, 1991-1993. Harlow: Longman Scientific & Technical. Pitman Res. Notes Math. Ser. 302, 113-124 (1994).
Summary: We provide a constructive proof of a result due to J. M. Ball and M. Slemrod [Commun. Pure Appl. Math. 32, 553-587 (1979; Zbl 0394.93041)] on localization of non harmonic asymptotically lacunary Fourier series. The new proof is based on some inequalities due to Ingham, and we use a similar technique to establish oscillation properties of some lacunary series. Both results are applied to the study of vibrating systems governed by an equation of the form \(u''+Au(t)=0\), where \(A\) is an elliptic operator of order 2 or 4.
For the entire collection see [Zbl 0795.00016].

35L25 Higher-order hyperbolic equations
35L10 Second-order hyperbolic equations
74H45 Vibrations in dynamical problems in solid mechanics
Zbl 0394.93041