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4 papers · 1 filter
Extensions of Positive Definite Functions: Applications and Their Harmonic Analysis
Palle Jorgensen, Steen Pedersen, Feng Tian
We study two classes of extension problems, and their interconnections: (i) Extension of positive definite (p.d.) continuous functions defined on subsets in locally compact groups…
Frames and Factorization of Graph Laplacians
Palle Jorgensen, Feng Tian
Using functions from electrical networks (graphs with resistors assigned to edges), we prove existence (with explicit formulas) of a canonical Parseval frame in the energy Hilbert…
Infinite networks and variation of conductance functions in discrete Laplacians
Palle Jorgensen, Feng Tian
For a given infinite connected graph and an arbitrary but fixed conductance function , we study an associated graph Laplacian ; it is a generalized difference o…
von Neumann indices and classes of positive definite functions
Palle Jorgensen, Feng Tian
With view to applications, we establish a correspondence between two problems: (i) the problem of finding continuous positive definite extensions of functions which are defined…