Abstract
In section 1.8 we studied the eigenvalues of the periodic, semi-periodic and twisted boundary-value problem on a period interval, and similarly those of a boundaryvalue problem with separated boundary conditions in section 2.3. We begin the present chapter with the observation that the eigenvalues and eigenfunctions of these boundary-value problems give rise to a generalisation of Fourier series convergent in the sense of a suitable Hilbert space. Thence we proceed to study the spectral properties of the periodic equation on the real line and on a half-line with a boundary condition of the separated type.
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© 2013 Springer Basel
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Brown, B.M., Eastham, M.S.P., Schmidt, K.M. (2013). Spectra. In: Periodic Differential Operators. Operator Theory: Advances and Applications, vol 230. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0528-5_4
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DOI: https://doi.org/10.1007/978-3-0348-0528-5_4
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Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-0527-8
Online ISBN: 978-3-0348-0528-5
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