Matches in SemOpenAlex for { <https://semopenalex.org/work/W4289785065> ?p ?o ?g. }
Showing items 1 to 61 of
61
with 100 items per page.
- W4289785065 abstract "The purpose of this article is to develop a Hadamard-Riesz type parametrix for the wave propagator in bounded planar domains with smooth, strictly convex boundary. This parametrix then allows us to rederive an oscillatory integral representation for the wave trace appearing in cite{MaMe82} and compute its principal symbol explicitly in terms of geometric data associated to the billiard map. This results in new formulas for the wave invariants. The order of the principal symbol, which appears to be inconsistent in the works of cite{MaMe82} and cite{Popov1994}, is also corrected. In those papers, the principal symbol was never actually computed and to our knowledge, this paper contains the first explicit formulas for the principal symbol of the wave trace. The wave trace formulas we provide are localized near both simple lengths corresponding to nondegenerate periodic orbits and degenerate lengths associated to one parameter families of periodic orbits tangent to a single rational caustic. Existence of a Hadamard-Riesz type parametrix with explicit symbol and phase calculations in the interior appears to be new in the literature, with the exception of the author's previous work cite{Vig18} in the special case of elliptical domains. This allows us to circumvent the symbol calculus in cite{DuGu75} and cite{HeZe12} when computing trace formulas, which are instead derived from integrating our explicit parametrix over the diagonal." @default.
- W4289785065 created "2022-08-04" @default.
- W4289785065 creator A5034671839 @default.
- W4289785065 date "2019-10-14" @default.
- W4289785065 modified "2023-09-29" @default.
- W4289785065 title "The Wave Trace and Birkhoff Billiards" @default.
- W4289785065 doi "https://doi.org/10.48550/arxiv.1910.06441" @default.
- W4289785065 hasPublicationYear "2019" @default.
- W4289785065 type Work @default.
- W4289785065 citedByCount "0" @default.
- W4289785065 crossrefType "posted-content" @default.
- W4289785065 hasAuthorship W4289785065A5034671839 @default.
- W4289785065 hasBestOaLocation W42897850651 @default.
- W4289785065 hasConcept C134306372 @default.
- W4289785065 hasConcept C134400042 @default.
- W4289785065 hasConcept C138885662 @default.
- W4289785065 hasConcept C18903297 @default.
- W4289785065 hasConcept C191832335 @default.
- W4289785065 hasConcept C199360897 @default.
- W4289785065 hasConcept C202444582 @default.
- W4289785065 hasConcept C2777299769 @default.
- W4289785065 hasConcept C33923547 @default.
- W4289785065 hasConcept C41008148 @default.
- W4289785065 hasConcept C41895202 @default.
- W4289785065 hasConcept C43929395 @default.
- W4289785065 hasConcept C60292330 @default.
- W4289785065 hasConcept C75291252 @default.
- W4289785065 hasConcept C86803240 @default.
- W4289785065 hasConcept C9012821 @default.
- W4289785065 hasConceptScore W4289785065C134306372 @default.
- W4289785065 hasConceptScore W4289785065C134400042 @default.
- W4289785065 hasConceptScore W4289785065C138885662 @default.
- W4289785065 hasConceptScore W4289785065C18903297 @default.
- W4289785065 hasConceptScore W4289785065C191832335 @default.
- W4289785065 hasConceptScore W4289785065C199360897 @default.
- W4289785065 hasConceptScore W4289785065C202444582 @default.
- W4289785065 hasConceptScore W4289785065C2777299769 @default.
- W4289785065 hasConceptScore W4289785065C33923547 @default.
- W4289785065 hasConceptScore W4289785065C41008148 @default.
- W4289785065 hasConceptScore W4289785065C41895202 @default.
- W4289785065 hasConceptScore W4289785065C43929395 @default.
- W4289785065 hasConceptScore W4289785065C60292330 @default.
- W4289785065 hasConceptScore W4289785065C75291252 @default.
- W4289785065 hasConceptScore W4289785065C86803240 @default.
- W4289785065 hasConceptScore W4289785065C9012821 @default.
- W4289785065 hasLocation W42897850651 @default.
- W4289785065 hasOpenAccess W4289785065 @default.
- W4289785065 hasPrimaryLocation W42897850651 @default.
- W4289785065 hasRelatedWork W21046731 @default.
- W4289785065 hasRelatedWork W35488379 @default.
- W4289785065 hasRelatedWork W44322554 @default.
- W4289785065 hasRelatedWork W44446963 @default.
- W4289785065 hasRelatedWork W45817336 @default.
- W4289785065 hasRelatedWork W473824 @default.
- W4289785065 hasRelatedWork W49201362 @default.
- W4289785065 hasRelatedWork W49910386 @default.
- W4289785065 hasRelatedWork W52736703 @default.
- W4289785065 hasRelatedWork W59395105 @default.
- W4289785065 isParatext "false" @default.
- W4289785065 isRetracted "false" @default.
- W4289785065 workType "article" @default.