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- W4313302813 abstract "A set $mathcal{S}$ of points in $mathbb{R}^n$ is called a rationally parameterisable hypersurface if $mathcal{S}={boldsymbol{sigma}(mathbf{t}): mathbf{t} in D}$, where $boldsymbol{sigma}: mathbb{R}^{n-1} rightarrow mathbb{R}^n$ is a vector function with domain $D$ and rational functions as components. A generalized $n$-dimensional polytope in $mathbb{R}^n$ is a union of a finite number of convex $n$-dimensional polytopes in $mathbb{R}^n$. The Fourier transform of such a generalized polytope $mathcal{P}$ in $mathbb{R}^n$ is defined by $F_{mathcal{P}}(mathbf{s})=int_{mathcal{P}} e^{-imathbf{s}cdotmathbf{x}} ,mathbf{dx}$. We prove that $F_{mathcal{P}_1}(boldsymbol{sigma}(mathbf{t})) = F_{mathcal{P}_2}(boldsymbol{sigma}(mathbf{t})) forall mathbf{t} in O$ implies $mathcal{P}_1=mathcal{P}_2$ if $O$ is an open subset of $D$ satisfying some well-defined conditions. Moreover we show that this theorem can be applied to quadric hypersurfaces that do not contain a line, but at least two points, i.e., in particular to spheres." @default.
- W4313302813 created "2023-01-06" @default.
- W4313302813 creator A5025619790 @default.
- W4313302813 date "2022-12-19" @default.
- W4313302813 modified "2023-09-26" @default.
- W4313302813 title "An Identity Theorem for the Fourier–Laplace Transform of Polytopes on Nonzero Complex Multiples of Rationally Parameterizable Hypersurfaces" @default.
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- W4313302813 doi "https://doi.org/10.1007/s00454-022-00467-9" @default.
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