期刊
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION
卷 30, 期 9-10, 页码 1098-1124出版社
TAYLOR & FRANCIS INC
DOI: 10.1080/01630560903408747
关键词
Fourier integral operators; Fourier series; Microlocal analysis; Pseudo-differential operators; Torus
资金
- EPSRC [EP/E062873/1, EP/G007233/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/G007233/1, EP/E062873/1] Funding Source: researchfish
On the torus, pseudo-differential operators can be presented globally by Fourier series, without local coordinate charts. Periodization of partial differential equations leads to investigating the correspondence between toroidal and Euclidean symbols of operators. Fourier series operatorsthe analogues of Fourier integral operatorsare introduced, and formulae for their compositions with pseudo-differential operators are presented. The L2 boundedness of pseudo-differential and Fourier series operators follows from certain conditions on phases and amplitudes.
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