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<div style="font-size: 13.3333330154419px;"><span style="font-size: 10pt; line-height: 15.3333320617676px; font-family: 'Segoe UI', sans-serif;">Sayin Liste Uyeleri,</span><br>
<br>
GTU Matematik Bölümü Genel Seminerleri kapsamında,<br>
17 Nisan Cuma günü saat 14:00'da <span style="font-size: 13.3199996948242px;">Deniz KARLI</span><br>
(Isık Universitesi) bir seminer verecektir. Seminerin<br>
detayları aşağıda olup tüm ilgilenenler davetlidir.<br>
<br>
Saygılarımızla,</div>
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<div style="background-color: white;"><font face="Tahoma" size="1"><span style="font-size: 13.31px;">Title: </span></font><font face="Tahoma" size="1"><span style="font-size: 13.31px;">Probabilistic Approach to Singular Integral Operators</span></font></div>
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<font face="Tahoma" size="1"><span style="font-size: 13.31px;">Abstract: Probability Theory has strong connections with many areas in Analysis. In </span></font><font face="Tahoma" size="1"><span style="font-size: 13.31px;">recent years, many classical results
have been restudied by Probabilists (e.g. </span></font><font face="Tahoma" size="1"><span style="font-size: 13.31px;">P.A. Meyer and N. Varopoulos) and alternative proofs have been introduced </span></font><font face="Tahoma" size="1"><span style="font-size: 13.31px;">using
powerful tools of Martingale Theory. In particular, one can use Brownian </span></font><font face="Tahoma" size="1"><span style="font-size: 13.31px;">Motion, a continuous stochastic process, to define harmonic functions in classical </span></font><font face="Tahoma" size="1"><span style="font-size: 13.31px;">sense.
In this talk, we replace Brownian Motion with a more general process, </span></font><font face="Tahoma" size="1"><span style="font-size: 13.31px;">namely a symmetric stable process. Stable processes are not continuous as </span></font><font face="Tahoma" size="1"><span style="font-size: 13.31px;">Brownian
Motion is. But they still enjoy many nice properties. Using this </span></font><font face="Tahoma" size="1"><span style="font-size: 13.31px;">process we define what a ”harmonic” function with respect to this process is </span></font><font face="Tahoma" size="1"><span style="font-size: 13.31px;">and
discuss operators obtained through these new ”harmonic” functions. </span></font><font face="Tahoma" size="1"><span style="font-size: 13.31px;">We will discuss some operators which are originated from classical Littlewood-</span></font><font face="Tahoma" size="1"><span style="font-size: 13.31px;">Paley
theory. They are used in analysis of singular integral operators. We </span></font><font face="Tahoma" size="1"><span style="font-size: 13.31px;">consider their modification with respect to this discontinuous stochastic process </span></font><font face="Tahoma" size="1"><span style="font-size: 13.31px;">to
generalise classic results. We discuss their boundedness on Lp spaces, and </span></font><font face="Tahoma" size="1"><span style="font-size: 13.31px;">discuss a multiplier theorem obtained through these new operators.</span></font></div>
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<div style="font-size: 13.3333330154419px;"><span style="font-size: 10pt; line-height: 15.3333320617676px; font-family: 'Segoe UI', sans-serif;">Dear all,</span><br>
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There will be a seminar in Gebze Technical University (GTU) on 17th of<br>
April by <span style="font-size: 13.3199996948242px;">Deniz KARLI</span> (Işık Uni) <br>
Time and place: At 14:00 in Department of Mathematics,<br>
Building I, Seminar room.</div>
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<div style="background-color: white;"><font face="Tahoma" size="1"><span style="font-size: 13.31px;">Title: </span></font><font face="Tahoma" size="1"><span style="font-size: 13.31px;">Probabilistic Approach to Singular Integral Operators</span></font></div>
</div>
<div style="font-family: Arial; font-size: 13.3333330154419px; background-color: white;">
<font face="Tahoma" size="1"><span style="font-size: 13.31px;"><br>
</span></font></div>
<div style="font-family: Arial; font-size: 13.3333330154419px; background-color: white;">
<font face="Tahoma" size="1"><span style="font-size: 13.31px;">Abstract: Probability Theory has strong connections with many areas in Analysis. In </span></font><font face="Tahoma" size="1"><span style="font-size: 13.31px;">recent years, many classical results
have been restudied by Probabilists (e.g. </span></font><font face="Tahoma" size="1"><span style="font-size: 13.31px;">P.A. Meyer and N. Varopoulos) and alternative proofs have been introduced </span></font><font face="Tahoma" size="1"><span style="font-size: 13.31px;">using
powerful tools of Martingale Theory. In particular, one can use Brownian </span></font><font face="Tahoma" size="1"><span style="font-size: 13.31px;">Motion, a continuous stochastic process, to define harmonic functions in classical </span></font><font face="Tahoma" size="1"><span style="font-size: 13.31px;">sense.
In this talk, we replace Brownian Motion with a more general process, </span></font><font face="Tahoma" size="1"><span style="font-size: 13.31px;">namely a symmetric stable process. Stable processes are not continuous as </span></font><font face="Tahoma" size="1"><span style="font-size: 13.31px;">Brownian
Motion is. But they still enjoy many nice properties. Using this </span></font><font face="Tahoma" size="1"><span style="font-size: 13.31px;">process we define what a ”harmonic” function with respect to this process is </span></font><font face="Tahoma" size="1"><span style="font-size: 13.31px;">and
discuss operators obtained through these new ”harmonic” functions. </span></font><font face="Tahoma" size="1"><span style="font-size: 13.31px;">We will discuss some operators which are originated from classical Littlewood-</span></font><font face="Tahoma" size="1"><span style="font-size: 13.31px;">Paley
theory. They are used in analysis of singular integral operators. We </span></font><font face="Tahoma" size="1"><span style="font-size: 13.31px;">consider their modification with respect to this discontinuous stochastic process </span></font><font face="Tahoma" size="1"><span style="font-size: 13.31px;">to
generalise classic results. We discuss their boundedness on Lp spaces, and </span></font><font face="Tahoma" size="1"><span style="font-size: 13.31px;">discuss a multiplier theorem obtained through these new operators.</span></font></div>
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