Explore the intricacies of fractional Laplacians in this 42-minute lecture by Alexander I. Nazarov, presented by the International Mathematical Union. Delve into the CS-extension and examine the restricted Dirichlet fractional Laplacian for & E (-1,0). Compare various fractional Laplacians in terms of quadratic forms and analyze the spectral Dirichlet and Neumann fractional Laplacians. Follow along as Nazarov presents proofs for Theorems 1, 2, and 3, and encounter a thought-provoking counterexample. Gain a deeper understanding of this complex mathematical concept through a comprehensive exploration of its diverse forms and applications.
Overview
Syllabus
Introduction
The CS-extension
The restricted Dirichlet FL for & E (-1,0)
The spectral Dirichlet and Neumann FLs for & E (-1,0)
Comparison of FLs in the sense of quadratic forms
Proof of Theorem 1
Proof of Theorem 2
A counterexample
Proof of Theorem 3
Taught by
International Mathematical Union
