Indicator function (complex analysis): Difference between revisions

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are called <math>\rho</math>-trigonometrically convex (<math>A</math> and <math>B</math> are real constants). If <math>\rho=1</math>, we simply say, that <math>h</math> is trigonometrically convex.

Such indicators have some special properties. For example, the following statements are all true for an indicator function that is trigonometrically convex at least on an interval <math>(\alpha,\beta)</math>:<ref name="Levin" />{{rp|55-57}}<ref name="Levin2" />{{rp|54-61}}:

* If <math>h(\theta_1)=-\infty</math> for a <math>\theta_1\in(\alpha,\beta)</math>, then <math>h=-\infty</math> everywhere in <math>(\alpha,\beta)</math>.