2025/05/28 by Edison Leguizamón, Carsten Trunk, Leguizamón, Edison +5
Mathematics · #34B45 #47A10 #47A75 #FOS: Mathematics #Graph theory and applications #Nonlinear Partial Differential Equations #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2505.22901
openalex publication_date 2025/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
On a star graph G with n = n+ + n- edges of unit length, we study the operator -(d2)/(d x2) on n+ and (d2)/(d x2) on n- edges equipped with Dirichlet boundary conditions at the outer vertices and a Kirchhoff condition at the central vertex. We study the spectral properties of the corresponding indefinite Kirchhoff Laplacian on G and we show that it is similar to a selfadjoint operator in the Hilbert space L2(G) and that its eigenfunctions form a Riesz basis. Furthermore, we give a complete description of the point spectrum.