For ER and s> 0, define 0 (x):= e-||||1/s, where ||||1= |x| ++ |n| is the...

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For ER and s> 0, define 0₁ (x):= e-||||1/s, where ||||1= |x₁| ++ |n| is the ₁ norm of a. For a lattice LCR", parameters > 0, and shift vector t ER", define Os (L-t) := Σe-||-t||₁1/s е YEL And, for r> 0, let Os,r (Lt):= Σ e-ly-t||1/s YEL,|y-t||zr Prove that for any lattice LCR", tER", parameter s > 0, and r > ns, Osr (L-t) ≤ (er/(ns))".e-¹/s.o₂(L). For ER and s> 0, define 0₁ (x):= e-||||1/s, where ||||1= |x₁| ++ |n| is the ₁ norm of a. For a lattice LCR", parameters > 0, and shift vector t ER", define Os (L-t) := Σe-||-t||₁1/s е YEL And, for r> 0, let Os,r (Lt):= Σ e-ly-t||1/s YEL,|y-t||zr Prove that for any lattice LCR", tER", parameter s > 0, and r > ns, Osr (L-t) ≤ (er/(ns))".e-¹/s.o₂(L).

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