Crest factor: Difference between revisions

Latest revision as of 17:49, 10 January 2015

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-In [[complex analysis]], '''Harnack's principle''' or '''Harnack's theorem''' is one of several closely related theorems about the convergence of sequences of [[harmonic function]]s, that follow from [[Harnack's inequality]].
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-If the [[function (mathematics)|functions]] <math> u_1(z)</math>, <math> u_2(z)</math>, ... are harmonic in an [[open connected subset]] <math>G</math> of the [[complex plane]] '''C''', and
-:<math>u_1(z) \le u_2(z) \le ...</math>
-in every point of <math>G</math>, then the [[Limit of a sequence|limit]]
-:<math> \lim_{n\to\infty}u_n(z)</math>
-either is infinite in every point of the [[domain (mathematics)|domain]]  <math>G</math> or it is finite in every point of the domain, in both cases uniformly in each [[compact space|compact]] subset of <math>G</math>. In the latter case, the function
-:<math> u(z) = \lim_{n\to\infty}u_n(z)</math>
-is harmonic in the set <math> G</math>.
-==References==
-*{{springer|id=h/h046620|title=Harnack theorem|first=L.I.|last= Kamynin}}
-*{{PlanetMath attribution|id=6657|title=Harnack's principle}}
-[[Category:Harmonic functions]]
-[[Category:Theorems in complex analysis]]
-[[Category:Mathematical principles]]

Crest factor: Difference between revisions

Latest revision as of 17:49, 10 January 2015

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