Abstract
Although the simplest version of spectral theory is found in matrix theory this is not its historic origin; that lies in the field of differential equations. Spectral theory for differential equations originates with the method of separation of variables, used to solve many of the (linear) equations of mathematical physics and leading directly to the problem of expanding an ‘arbitrary’ function in terms of eigenfunctions of the reduced equation. This is the central problem of spectral theory.
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Bennewitz, C., Brown, M., Weikard, R. (2020). Introduction. In: Spectral and Scattering Theory for Ordinary Differential Equations. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-030-59088-8_1
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DOI: https://doi.org/10.1007/978-3-030-59088-8_1
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