1 citations · 1 across the 6 of their papers we have counts for
11 papers
The spectral geometry of biregular graphs: a quantum graph approach
Robert Carlson
The spectral theory of the Laplace differential operator for biregular quantum graphs is developed. Trees are studied in detail. Generating functions for closed non backtracking wa…
Robin boundary conditions for the Laplacian on metric graph completions
Robert Carlson
A generalization of Robin boundary conditions leading to self-adjoint operators is developed for the second derivative operator on metric graphs with compact completion and totally…
Metric Graphs with Totally Disconnected Boundary
Robert Carlson
Boundary analysis is developed for a rich class of generally infinite weighted graphs with compact metric completions. These graph completions have totally disconnected boundaries.…
Analytic Differential Operators on the Unit Disk
Robert Carlson
Formally symmetric differential operators on weighted Hardy-Hilbert spaces are analyzed, along with adjoint pairs of differential operators. Eigenvalue problems for such operators…
Eigenfunctions of Periodic Differential Operators Analytic in a Strip
Robert Carlson
Ordinary differential operators with periodic coefficients analytic in a strip act on a Hardy-Hilbert space of analytic functions with inner product defined by integration over a p…
An Extended Pruess Method for Sturm-Liouville Problems
Robert Carlson
A new version of the piecewise approximation (Pruess) method is developed for calculating eigenvalues of Sturm-Liouville problems. The usual piecewise constant or piecewise linear…
Quantum Cayley graphs for free groups
Robert Carlson
Differential operators of Schrodinger type are considered on metric Cayley graphs of free groups with a minimal set of M generators. The potential and edge lengths may vary with th…
Myopic Models of Population Dynamics on Infinite Networks
Robert Carlson
Reaction-diffusion equations are treated on infinite networks using semigroup methods. To blend high fidelity local analysis with coarse remote modeling, initial data and solutions…
After the Explosion: Dirichlet Forms and Boundary Problems for Infinite Graphs
Robert Carlson
Formal Laplace operators are analyzed for a large class of resistance networks with vertex weights. The graphs are completed with respect to the minimal resistance path metric. Com…
Dirichlet to Neumann Maps for Infinite Quantum Graphs
Robert Carlson
The Dirichlet problem and Dirichlet to Neumann map are analyzed for elliptic equations on a large collection of infinite quantum graphs. For a dense set of continuous functions on…
The Continuous Graph FFT
Robert Carlson
The discrete Fourier transform and the FFT algorithm are extended from the circle to continuous graphs with equal edge lengths.