(Bi)-orthogonality relation for eigenfunctions of self-adjoint operators | Zendy

L S Ledet | Zendy; S. V. Sorokin | Zendy

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(Bi)-orthogonality relation for eigenfunctions of self-adjoint operators

Author(s) -

L S Ledet,

S. V. Sorokin

Publication year - 2019

Publication title -

philosophical transactions of the royal society a mathematical physical and engineering sciences

Language(s) - English

Resource type - Journals

eISSN - 1471-2962

pISSN - 1364-503X

DOI - 10.1098/rsta.2019.0112

Subject(s) - eigenfunction , orthogonality , relation (database) , mathematics , self adjoint operator , mathematical analysis , pure mathematics , physics , computer science , geometry , eigenvalues and eigenvectors , hilbert space , quantum mechanics , database

The bi-orthogonality relation for eigenfunctions of self-adjoint operators is derived. Its composition is explained in view of the structure of a characteristic equation and of the energy flow components. Application of the bi-orthogonality relation for solving forcing problems is generalized and the connection between the bi-orthogonality relation and the virtual wave method is highlighted. Technicalities are illustrated in a non-trivial example of propagation of free/forced cylindrical waves in a thin elastic plate under heavy fluid loading. This article is part of the theme issue ‘Modelling of dynamic phenomena and localization in structured media (part 1)’.

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