Abstract
Stationary fields and their generalizations play an important role in modeling of various biological, physical, geological and economical phenomena and give rise to various methods for forecasting, approximation and (machine) learning. Many modern techniques rely on spectral representations of the underlying models. The aim of this note is to give a short historical survey on the spectral theory of stationary fields, fields with stationary increments and intrinsically stationary fields. These random fields are closely related to unitary representations in Pontryagin spaces. In this context H. Langer and M.G. Kreĭn devoted several papers especially to continuation problems related to intrinsically stationary fields.
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Berschneider, G., Sasvári, Z. (2018). Spectral Theory of Stationary Random Fields and their Generalizations. A Short Historical Survey. In: Alpay, D., Kirstein, B. (eds) Indefinite Inner Product Spaces, Schur Analysis, and Differential Equations. Operator Theory: Advances and Applications(), vol 263. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-68849-7_8
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