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<P class=MsoTitle style="MARGIN: 0cm 0cm 0pt" align=center><SPAN
style="FONT-SIZE: 18pt; FONT-FAMILY: 'Times New Roman','serif'"><STRONG><U>SEMINARIO
DI <SPAN style="mso-no-proof: yes">MATEMATICA</SPAN><?xml:namespace prefix = o
ns = "urn:schemas-microsoft-com:office:office"
/><o:p></o:p></U></STRONG></SPAN></P>
<H2 style="MARGIN: 0cm 0cm 0pt 9pt" align=center><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; mso-no-proof: yes"></SPAN> </H2>
<H2 style="MARGIN: 0cm 0cm 0pt 9pt" align=center><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; mso-no-proof: yes">Lunedì 23
gennaio 2012</SPAN><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'"><o:p></o:p></SPAN></H2>
<P class=MsoNormal
style="MARGIN: 0cm 0cm 0pt 9pt; LINE-HEIGHT: 18pt; TEXT-ALIGN: center; tab-stops: 324.0pt"
align=center><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'">Ore <SPAN
style="mso-no-proof: yes">16.00</SPAN><o:p></o:p></SPAN></P>
<P class=MsoNormal
style="MARGIN: 0cm 0cm 0pt 9pt; LINE-HEIGHT: 18pt; TEXT-ALIGN: center; tab-stops: 324.0pt"
align=center><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'"><o:p> </o:p></SPAN></P>
<P class=MsoNormal
style="MARGIN: 0cm 0cm 0pt 9pt; LINE-HEIGHT: 18pt; TEXT-ALIGN: center; tab-stops: 324.0pt"
align=center><U><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'">Scuola Normale
Superiore<o:p></o:p></SPAN></U></P>
<P class=MsoNormal
style="MARGIN: 0cm 0cm 0pt 9pt; LINE-HEIGHT: 18pt; TEXT-ALIGN: center; tab-stops: 324.0pt"
align=center><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'">Pisa<o:p></o:p></SPAN></P>
<P class=MsoNormal
style="MARGIN: 0cm 0cm 0pt 9pt; LINE-HEIGHT: 18pt; TEXT-ALIGN: center; tab-stops: 324.0pt"
align=center><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'">Aula <SPAN
style="mso-no-proof: yes">2</SPAN><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: center"
align=center><B style="mso-bidi-font-weight: normal"><SPAN lang=EN-US
style="FONT-SIZE: 24pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-US"></SPAN></B> </P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: center"
align=center><B style="mso-bidi-font-weight: normal"><SPAN lang=EN-US
style="FONT-SIZE: 24pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-US">Sanjiv
Kumar Gupta <I style="mso-bidi-font-style: normal"><SPAN
style="mso-no-proof: yes"><o:p></o:p></SPAN></I></SPAN></B></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: center"
align=center><I style="mso-bidi-font-style: normal"><SPAN lang=EN-US
style="FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-US"><FONT
size=3>University of Muscat<o:p></o:p></FONT></SPAN></I></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><SPAN lang=EN-US
style="FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-US"><o:p><FONT
size=3> </FONT></o:p></SPAN></P>
<P class=MsoNormal
style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: center; tab-stops: 324.0pt"
align=center><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'">Terrà un
seminario dal titolo:<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; tab-stops: 324.0pt"><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'"><o:p><FONT
size=3> </FONT></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: center"
align=center><B style="mso-bidi-font-weight: normal"><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-GB
style="FONT-SIZE: 24pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-GB">“</SPAN></I></B><B
style="mso-bidi-font-weight: normal"><SPAN lang=EN-US
style="FONT-SIZE: 24pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-US">The
smoothness of convolutions of zonal measures on symmetric spaces</SPAN></B><B
style="mso-bidi-font-weight: normal"><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-GB
style="FONT-SIZE: 24pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-GB">”</SPAN></I></B><B
style="mso-bidi-font-weight: normal"><SPAN lang=EN-US
style="FONT-SIZE: 24pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-US"><o:p></o:p></SPAN></B></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><B
style="mso-bidi-font-weight: normal"><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-GB
style="FONT-SIZE: 10pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-GB"><o:p> </o:p></SPAN></I></B></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><B
style="mso-bidi-font-weight: normal"><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-GB
style="FONT-SIZE: 10pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-GB">Abstract:<o:p></o:p></SPAN></I></B></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><B
style="mso-bidi-font-weight: normal"><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-GB
style="FONT-SIZE: 10pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-GB"><o:p> </o:p></SPAN></I></B></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><SPAN
lang=EN-US
style="FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-US"><FONT
size=3>Suppose G is a compact, simple Lie group with Cartan involution \theta
and K is the compact subgroup of G fixed by \theta. Then G/K is a compact
symmetric space. Dunkl proved that the convolution of the surface measure of the
sphere in R<SUP>n</SUP> with itself is absolutely continuous with respect to
Lebesgue measure on R<SUP>n</SUP>. Generalizing this, Ragozin<SPAN
style="mso-spacerun: yes"> </SPAN>proved that if
\mu<SUB>1</SUB>,...,\mu<SUB>dim(G/K)</SUB> are any K-bi-invariant continuous
measures on G, then \mu<SUB>1</SUB>*....*\mu<SUB>dim(G/K)</SUB> is absolutely
continuous with respect to the Haar measure on G. <o:p></o:p></FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><SPAN
lang=EN-US
style="FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-US"><FONT
size=3>In this talk, it<SPAN style="mso-spacerun: yes"> </SPAN>will shown
that if r=rank(G/K), and \mu_1,...,\mu<SUB>2r+1</SUB> are any K-bi-invariant
continuous measures on G, then \mu<SUB>1</SUB>*...*\mu<SUB>2r+1</SUB> is
absolutely continuous with respect to the Haar measure on G. I will also talk on
some related results about noncompact symmetric space and about other
K-invariant measures. This is joint work with Kathryn
Hare.<o:p></o:p></FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-US
style="FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-US"><o:p><FONT
size=3> </FONT></o:p></SPAN></I></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><SPAN lang=EN-US
style="FONT-SIZE: 14.5pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-US"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><B
style="mso-bidi-font-weight: normal"><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-US
style="FONT-SIZE: 10pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-US"><o:p> </o:p></SPAN></I></B></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'">Tutti gli
interessati sono invitati a partecipare.<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'"><o:p> </o:p></SPAN></P>
<P class=Corpodeltesto1 style="MARGIN: 0cm 0cm 0pt; tab-stops: 9.0cm"><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: IT"><SPAN
style="mso-tab-count: 2"> </SPAN></SPAN><FONT
face="Times New Roman"><SPAN style="mso-ansi-language: IT"><SPAN
style="mso-tab-count: 2"><FONT size=3> </FONT></SPAN></SPAN><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: IT">Classe
di Scienze</P></SPAN></FONT></FONT></DIV>
<DIV><FONT face=Arial
size=2>--------------------------------------------------------------------------------<BR>Valeria
Giuliani<BR>Scuola Normale Superiore<BR>Servizio Supporto Attività
Didattiche<BR>Tel. 050-509260<BR>Fax. 050-509045<BR>Piazza dei Cavalieri,
7<BR>56126 Pisa<BR>E-Mail: <A
href="mailto:v.giuliani@sns.it">v.giuliani@sns.it</A> <BR>E-Mail: <A
href="mailto:segreteria.scienze@sns.it">segreteria.scienze@sns.it</A></FONT></DIV>
<DIV> </DIV>
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distruggerla.<BR>Grazie.</FONT></DIV>
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