An Inverse Spectral Result for the Periodic Euler-Bernoulli Equation

Papanicolaou, VG

dc.contributor.author	Papanicolaou, VG	en
dc.date.accessioned	2014-03-01T01:19:54Z
dc.date.available	2014-03-01T01:19:54Z
dc.date.issued	2004	en
dc.identifier.issn	0022-2518	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/15756
dc.subject	Euler-Bernoulli (or beam) operator/equation	en
dc.subject	Floquet theory	en
dc.subject	Hill's operator, periodic coefficients	en
dc.subject	Inverse periodic spectral theory	en
dc.subject	Multipoint eigenvalue problem	en
dc.subject	Pseudospectrum	en
dc.subject	Spectrum	en
dc.subject.classification	Mathematics	en
dc.subject.other	MATRIX HILLS EQUATION	en
dc.subject.other	SYSTEMS	en
dc.title	An Inverse Spectral Result for the Periodic Euler-Bernoulli Equation	en
heal.type	journalArticle	en
heal.identifier.primary	10.1512/iumj.2004.53.2493	en
heal.identifier.secondary	http://dx.doi.org/10.1512/iumj.2004.53.2493	en
heal.language	English	en
heal.publicationDate	2004	en
heal.abstract	The Floquet (direct spectral) theory of the periodic Euler-Bernoulli equation has been developed by the author in [19], [21], and [20], Here we begin a systematic study of the inverse periodic spectral theory, in the spirit of the corresponding theory of the second-order operator, namely the Hill's operator. Our main result is that, if there are no pseudogaps (equivalently, if the Bloch-Floquet variety is reducible in a certain sense), then the Euler-Bernoulli operator is the square of a second-order (Hill-type) operator. This result had been conjectured by the author, in his earlier works.	en
heal.publisher	INDIANA UNIV MATH JOURNAL	en
heal.journalName	Indiana University Mathematics Journal	en
dc.identifier.doi	10.1512/iumj.2004.53.2493	en
dc.identifier.isi	ISI:000220775800011	en
dc.identifier.volume	53	en
dc.identifier.issue	1	en
dc.identifier.spage	223	en
dc.identifier.epage	242	en