ON A CONVOLUTION FOR q-NORMAL ELEMENTS

Kula A; Ricard E

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ON A CONVOLUTION FOR q-NORMAL ELEMENTS

机译：关于q范数元素的卷积

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In 2000 Carnovale and Koornwinder defined a q-convolution and proved that for some classes of measures it is associative and commutative. We investigate its positivity preserving properties. One of them is the notion of q-positivity related to q-moments. In this paper we describe an algebraic interpretation of q-positivity which leads us to the definition of (p, q)-convolution. It has a form similar to the q-convolution of Carnovale and Koornwinder coming from a braided algebra. For the new convolution we find an appropriate analogue of Fourier transform and also present a central limit theorem.

机译：在2000年，Carnovale和Koornwinder定义了q卷积，并证明了对于某些类的测度，它是关联的和可交换的。我们调查其积极性保存属性。其中之一是与q矩有关的q正性的概念。在本文中，我们描述了对q正性的代数解释，这使我们得出（p，q）-卷积的定义。它的形式类似于来自编织代数的Carnovale和Koornwinder的q卷积。对于新的卷积，我们找到了适当的傅立叶变换类似物，并且还提出了一个中心极限定理。

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《Infinite dimensional analysis, quantum probability, and related topics》 |2008年第4期|共24页
作者
Kula A; Ricard E;
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正文语种 eng
中图分类物理学;
关键词
Convolution; positive definiteness; q-normal elements; non-commutative central limit theorem; OPERATORS;

机译：卷积;正定性;q-正规元素;非交换中心极限定理;算子;

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ON A CONVOLUTION FOR q-NORMAL ELEMENTS

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