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CATEGORIES:Academics,Lectures & conferences
DESCRIPTION:Abstract. The existence of eigenfunctions of fractional Laplac
ian with homogeneous zero boundary condition has been well-known a long tim
e ago\, however\, how to write out their analytic expressions is a challeng
ing task. In this presentation\, I will focus on the 1-dimensional case onl
y and provide a potential way to obtain the analytic eigenfunctions. We wil
l show the spectral problem of 1-D fractional Laplacian is equivalent to th
e spectrum problem of double-sided Riemann-Liouville fractional diffusion d
erivatives. By using the latter\, we turn the fractional differential equat
ion into the singular integral equation involving the Hilbert transform\, f
rom which the eigenfunctions can be solved informally. Lastly\, some open q
uestions of this ongoing work will be shared as well.
DTEND:20240202T190000Z
DTSTAMP:20240714T051815Z
DTSTART:20240202T180000Z
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SUMMARY:What are the analytic eigenfunctions of 1-D fractional Laplacian? w
ith Yulong Li
UID:tag:localist.com\,2008:EventInstance_45500185025940
URL:https://calendar.fiu.edu/event/what_are_the_analytic_eigenfunctions_of_
1-d_fractional_laplacian_with_yulong_li
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