 Compact embedding of the harmonic-oscillator energy space

ID: compact-embedding-of-the-harmonic-oscillator-energy-space

Σ ↪ L^{2} (R^{d})

is compact. Rellich compactness controls a fixed ball, while

\int_{∣ x ∣ > R} ∣ v ∣^{2} \leq R^{- 2} ∥∣ x ∣ v ∥_{2}^{2}

controls the tail uniformly.

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