MULTIPLICATION OPERATORS ON THE ENERGY SPACE

作者：Jorgensen Palle E T^*; Pearse Erin P J

来源：Journal of Operator Theory, 2013, 69(1): 135-159.

DOI：10.7900/jot.2010jul20.1886

• Multiplication operator
• Dirichlet form
• graph energy
• discrete potential theory
• graph Laplacian
• weighted graph
• spectral graph theory
• resistance network
• Gel%26apos
• fand space
• reproducing kernel Hilbert space

We consider the multiplication operators on H-epsilon (the space of functions of finite energy supported on an infinite network), characterize them in terms of positive semidefinite functions. We show why they are typically not self-adjoint, and compute their adjoints in terms of a reproducing kernel. We also consider the bounded elements of H-epsilon and use the (possibly unbounded) multiplication operators corresponding to them to construct a boundary theory for the network. In the case when the only harmonic functions of finite energy are constant, we show that the corresponding Gel%26apos;fand space is the 1-point compactification of the underlying network.

• 出版日期2013