LAUSR

Here we deal with the following question: Is it true that, for any closed interval on the real line ℝ that does not contain the origin, there exists a characteristic function f such that f(x) coincides with the normal characteristic function e−x2/2$$ {\mathrm{e}}^{-{x}^2/2} $$ on this interval but f(x) ≢ e−x2/2$$ {\mathrm{e}}^{-{x}^2/2} $$ on ℝ? The answer to this question is positive. We study a more general case of an arbitrary characteristic function g of a continuous probability density, instead of e−x2/2$$ {\mathrm{e}}^{-{x}^2/2} $$.