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Generalized uncertainty inequalities

Authors:

Alessio Martini

Institution:

1. Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126, Pisa, Italy

Abstract:

The Heisenberg–Pauli–Weyl (HPW) uncertainty inequality on \mathbbRⁿ{\mathbb{R}^n} says that

\|\| f \|\|₂ ￡ C_a,b\|\| \|x\|^a f\|\|₂^\fracba+b\|\| (-D)^b/2f\|\|₂^\fracaa+b.\\| f \\|_2 \leq C_{\alpha,\beta}\\| \|x\|^\alpha f\\|_2^\frac{\beta}{\alpha+\beta}\\| (-\Delta)^{\beta/2}f\\|_2^\frac{\alpha}{\alpha+\beta}.

Keywords:
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