<oai_dc:dc xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd">
<dc:title>Monotone and boolean convolutions for non-compactly supported probability measures</dc:title>
<dc:creator>Uwe Franz</dc:creator>
<dc:subject>46L53</dc:subject><dc:subject>46L54</dc:subject><dc:subject>47D40</dc:subject><dc:subject>60E07</dc:subject><dc:subject>81Q10</dc:subject><dc:subject>monotone independence</dc:subject><dc:subject>monotone convolution</dc:subject><dc:subject>boolean independence</dc:subject><dc:subject>boolean convolution</dc:subject><dc:subject>unbounded operators</dc:subject>
<dc:description>The equivalence of the characteristic function approach and the probabilistic approach to monotone and boolean convolutions is proven for non-compactly supported probability measures. A probabilistically motivated definition of the multiplicative boolean convolution of probability measures on the positive half-line is proposed. Unlike Bercovici&#39;s multiplicative boolean convolution it is always defined, but it turns out to be neither commutative nor associative. Finally some relations between free, monotone, and boolean convolutions are discussed.</dc:description>
<dc:publisher>Indiana University Mathematics Journal</dc:publisher>
<dc:date>2009</dc:date>
<dc:type>text</dc:type>
<dc:format>pdf</dc:format>
<dc:identifier>10.1512/iumj.2009.58.3578</dc:identifier>
<dc:source>10.1512/iumj.2009.58.3578</dc:source>
<dc:language>en</dc:language>
<dc:relation>Indiana Univ. Math. J. 58 (2009) 1151 - 1186</dc:relation>
<dc:coverage>state-of-the-art mathematics</dc:coverage>
<dc:rights>http://iumj.org/access/</dc:rights>
</oai_dc:dc>