can someone explain the physical meaning of an analytic semigroup of linear bounded operators? Why are they important with respect to the strongly continuous case?
2026-03-28 00:36:56.1774658216
Analytic semigroups of linear operators
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Analytic semigroups are often related to parabolic equations. The prototype example is the heat equation (more generally diffusion equations). The analyticity of the semigroup means in particular that the solution is smooth (analytic) for positive times. This fact is physically interpreted by a smoothing effect of the heat far away from zero even for non-smooth initial conditions (initial temperatures).