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We find logarithmic asymptotics of    L  2   ‐small deviation probabilities for weighted stationary Gaussian processes (both for real and complex‐valued) having a power‐type discrete or continuous spectrum. Our results are based on the spectral theory of pseudo‐differential operators developed by Birman and Solomyak.

L 2 ‐SMALL DEVIATIONS FOR WEIGHTED STATIONARY PROCESSES