Fourier integral operators of infinite order on \({\mathcal D}_{L^2}^{\{\sigma\}}({\mathcal D}_{L^2}^{\{\sigma\}'})\) with an application to a certain Cauchy problem (Q1174515)
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scientific article; zbMATH DE number 8967
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Fourier integral operators of infinite order on \({\mathcal D}_{L^2}^{\{\sigma\}}({\mathcal D}_{L^2}^{\{\sigma\}'})\) with an application to a certain Cauchy problem |
scientific article; zbMATH DE number 8967 |
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Fourier integral operators of infinite order on \({\mathcal D}_{L^2}^{\{\sigma\}}({\mathcal D}_{L^2}^{\{\sigma\}'})\) with an application to a certain Cauchy problem (English)
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25 June 1992
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The author develops a calculus of Fourier integral operators of infinite order in the spaces \({\mathcal D}^{\{\sigma\}}_{L^ 2} ({\mathcal D}^{\{\sigma\}'}_{L^ 2})\). The calculus is then applied to the Cauchy problem for the operator \(P=\partial_ t-i\lambda(t,x,D_ x)+a(t,x,D_ x)\), where \(\lambda,a\) are pseudo-differential operators. Some sufficient conditions for well-posedness of this Cauchy problem are proved.
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Fourier integral operators
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Cauchy problem
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pseudo-differential operators
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well-posedness
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