The spectrum of a distribution function is related to the quasi-analyticity of a class of functions <mml:math alttext="$\left\{ {CM_{\left( j \right)} } \right\}$" id="E1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mi>C</mml:mi><mml:msub><mml:mi>M</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>j</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:mrow></mml:math>, where <mml:math alttext="$M_{\left( j \right)} $" id="E2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>j</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:math> is a multisequence of positive numbers. For a regular multisequence, a result on the uniqueness of characteristic function decomposition is given.

International Journal of Mathematics and Mathematical Sciences

On the spectrum of a distribution function and on unique factorization

Abstract

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