Abstract:We prove Szegő-type trace asymptotics for translation-invariant operators on polygons. More precisely, consider a Fourier multiplier = * on 2 ( ℝ 2 ) with a sufficiently decaying, smooth symbol ∶ ℝ 2 → ℂ. Let ⊂ ℝ 2 be the interior of a polygon and, for ≥ 1, define its scaled version ∶= ⋅ . Then we study the spectral asymptotics for the operator = , the spatial restriction of onto : for entire functions ℎ with ℎ(0) = 0 we provide a complete asymptotic expansion of trℎ ( ) as → ∞. These trace asymptotics con… Show more
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