Spectral Determinant for the Damped Wave Equation on an Interval |
| P. Freitasa, b, J. Lipovskýc
aDepartamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1, P-1049-001 Lisboa, Portugal bGrupo de Física Matemática, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, Edifício C6, P-1749-016 Lisboa, Portugal cDepartment of Physics, Faculty of Science, University of Hradec Králové, Rokitanského 62, 500,03 Hradec Králové, Czech Republic |
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| We evaluate the spectral determinant for the damped wave equation on an interval of length T with Dirichlet boundary conditions, proving that it does not depend on the damping. This result is achieved by analysing the square of the damped wave operator using the general result by Burghelea, Friedlander, and Kappeler on the determinant for a differential operator with matrix coefficients. |
DOI:10.12693/APhysPolA.136.817 PACS numbers: 46.40.Ff, 03.65.Ge |