Spectral Invariants of Integrable Polygons
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| Název: | Spectral Invariants of Integrable Polygons |
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| Autoři: | Mårdby, Gustav, 1999, Rowlett, Julie, 1978 |
| Zdroj: | Journal of Fourier Analysis and Applications. 31(6) |
| Témata: | Polygonal billiard, Helmholtz equation, Zeta-regularized determinant, Laplace eigenvalues, Closed geodesic, Polygonal domain, Heat trace, Laplace spectrum, Spectral zeta function |
| Popis: | An integrable polygon is one whose interior angles are fractions of π; that is to say of the form π n for positive integers n. We consider the Laplace spectrum on these polygons with the Dirichlet and Neumann boundary conditions, and we obtain new spectral invariants for these polygons. This includes new expressions for the spectral zeta function and zeta-regularized determinant as well as a new spectral invariant contained in the short-time asymptotic expansion of the heat trace. Moreover, we demonstrate relationships between the short-time heat trace invariants of general polygonal domains (not necessarily integrable) and smoothly bounded domains and pose conjectures and further related directions of investigation. |
| Popis souboru: | electronic |
| Přístupová URL adresa: | https://research.chalmers.se/publication/549109 https://research.chalmers.se/publication/549109/file/549109_Fulltext.pdf |
| Databáze: | SwePub |
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Nájsť tento článok vo Web of Science | Abstrakt: | An integrable polygon is one whose interior angles are fractions of π; that is to say of the form π n for positive integers n. We consider the Laplace spectrum on these polygons with the Dirichlet and Neumann boundary conditions, and we obtain new spectral invariants for these polygons. This includes new expressions for the spectral zeta function and zeta-regularized determinant as well as a new spectral invariant contained in the short-time asymptotic expansion of the heat trace. Moreover, we demonstrate relationships between the short-time heat trace invariants of general polygonal domains (not necessarily integrable) and smoothly bounded domains and pose conjectures and further related directions of investigation. |
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| ISSN: | 15315851 10695869 |
| DOI: | 10.1007/s00041-025-10202-6 |