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.