Equivalences are established between common conditions on the characteristic exponent and the time behavior of the density supremum for vaguely continuous convolution semigroups on R^d, together with qualitative lower estimates under mild assumptions.
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L{\'e}vy processes: concentration function and heat kernel bounds
Equivalences are established between common conditions on the characteristic exponent and the time behavior of the density supremum for vaguely continuous convolution semigroups on R^d, together with qualitative lower estimates under mild assumptions.