Colloquium| Institute of Mathematical Sciences
Time：14:00-15:00, November 21 Thursday
Location：Room S408, IMS
Speaker: Chen Huyan, New York University Shanghai
Abstract: In this talk, we study the logarithmic Laplacian operator L∆, which is a singular integral operator with symbol 2log|ζ|. We show that this operator has the integral representation
with
) and 
, where Γ is the Gamma function,
is the Digamma function and
(1) is the Euler Mascheroni constant. This operator arises as formal derivative
of fractional Laplacians at s = 0. We develop the functional analytic framework for Dirichlet problems involving the logarithmic Laplacian on bounded domains and use it to characterize the asymptotics of principal Dirichlet eigenvalues and eigenfunctions of (−∆)s as s → 0.