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Gaps in the essential spectrum of periodic elastic waveguides
Author(s) -
Cardone C.,
Minutolo V.,
Nazarov S.A.
Publication year - 2009
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200800221
Subject(s) - essential spectrum , spectrum (functional analysis) , eigenvalues and eigenvectors , discrete spectrum , interval (graph theory) , symmetry (geometry) , point (geometry) , mathematics , mathematical analysis , frequency spectrum , type (biology) , broad spectrum , physics , pure mathematics , quantum mechanics , optics , geometry , combinatorics , chemistry , ecology , biology , spectrum analyzer , combinatorial chemistry
Abstract Examples of periodic elastic waveguides are constructed, the essential spectrum of which has a gap, i.e. an open interval in the positive real semiaxis intersecting with the discrete spectrum only. The gap is detected with the help of an inequality of Korn's type and the max‐min principle for eigenvalues of self‐adjoint positive operators. Under a certain symmetry assumption, it is demonstrated that the first band of the essential spectrum can include eigenvalues in the point spectrum.