2017/07/10 by Delgado, Julio, Ruzhansky, Michael
#22E30 #35S05 #47B06 #47B10 (Secondary) #58J40 (Primary) #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Spectral Theory (math.SP)
paper · doi:10.48550/arxiv.1707.03062
This is a survey on a notion of invariant operators, or Fourier multipliers on Hilbert spaces. This concept is defined with respect to a fixed partition of the space into a direct sum of finite dimensional subspaces. In particular this notion can be applied to the important case of L2(M) where M is a compact manifold M endowed with a positive measure. The partition in this case comes from the spectral properties of a a fixed elliptic operator E.