39 citations · 123 across the 23 of their papers we have counts for
10 papers · 1 filter
Symmetric pairs and self-adjoint extensions of operators, with applications to energy networks
Palle E. T. Jorgensen, Erin P. J. Pearse
We provide a streamlined construction of the Friedrichs extension of a densely-defined self-adjoint and semibounded operator on a Hilbert space , by means of a sym…
Symmetric pairs of unbounded operators in Hilbert space, and their applications in mathematical physics
Palle E. T. Jorgensen, Erin P. J. Pearse
In a previous paper, the authors introduced the idea of a symmetric pair of operators as a way to compute self-adjoint extensions of symmetric operators. In brief, a symmetric pair…
Unbounded operators in Hilbert space, duality rules, characteristic projections, and their applications
Palle Jorgensen, Erin Pearse, Feng Tian
Our main theorem is in the generality of the axioms of Hilbert space, and the theory of unbounded operators. Consider two Hilbert spaces such that their intersection contains a fix…
Unbounded containment in the energy space of a network and the Krein extension of the energy Laplacian
Palle E. T. Jorgensen, Erin P. J. Pearse
We compare the space of square-summable functions on an infinite graph (denoted ) with the space of functions of finite energy (denoted ). The…
Spectral comparisons between networks with different conductance functions
Palle E. T. Jorgensen, Erin P. J. Pearse
For a network consisting of a graph with edge weights prescribed by a given conductance function , we consider the effects of replacing these weights with a new function tha…
Spectral reciprocity and matrix representations of unbounded operators
Palle E. T. Jorgensen, Erin P. J. Pearse
Motivated by potential theory on discrete spaces, we study a family of unbounded Hermitian operators in Hilbert space which generalize the usual graph-theoretic discrete Laplacian.…
Resistance boundaries of infinite networks
Palle E. T. Jorgensen, Erin P. J. Pearse
A resistance network is a connected graph . The conductance function weights the edges, which are then interpreted as conductors of possibly varying strengths. The…
Gel'fand triples and boundaries of infinite networks
Palle E. T. Jorgensen, Erin P. J. Pearse
We study the boundary theory of a connected weighted graph from the viewpoint of stochastic integration. For the Hilbert space \HE of Dirichlet-finite functions on , we cons…
A Hilbert space approach to effective resistance metric
Palle E. T. Jorgensen, Erin P. J. Pearse
A resistance network is a connected graph . The conductance function weights the edges, which are then interpreted as conductors of possibly varying strengths. The…
A discrete Gauss-Green identity for unbounded Laplace operators and transience of random walks
Palle E. T. Jorgensen, Erin P. J. Pearse
A resistance network is a connected graph . The conductance function weights the edges, which are then interpreted as resistors of possibly varying strengths. The r…