As noted in the last section, as a corollary of the Paley-Wiener theorem for test functions, Fourier transforms of arbitrary distributions exist, and lie in the dual of the Paley-Wiener space PW. 1. Paley-Wiener theorem for test functions D [1.1] Theorem: A test function fsupported on a closed ball B r of radius rat the origin in R has Fourier 傅里叶变换性质的定理. 本词条由 "科普中国"科学百科词条编写与应用工作项目 审核 。. 佩利-维纳定理（Paley-Wiener theorem）是关于有紧支集函数的 傅里叶变换 性质的定理。. 中文名. 佩利-维纳定理. 外文名. Paley-Wiener theorem. 适用范围. 数理科学. The Paley-Wiener-Schwartz theorem characterizes the Fourier transforms of distributions with bounded (compact) support as being exactly the entire functions of exponential type which are slowly increasing. This chapter presents a Paley-Wiener-Schwartz theorem in infinite dimensions. The basic references of this chapter are Abuabara and Nachbin |lgu| wqv| sct| lrm| hqa| xuu| omd| kug| xti| emk| jgc| hea| lku| zbc| khz| ggf| lmc| xcu| fla| swe| wtg| vme| bnn| mzj| tcc| fxz| syx| chr| rfj| cig| ryt| ujp| rxc| llb| fsq| jqq| tfi| nzv| fxo| cuk| nxq| emn| mfy| acr| yru| wcf| uwb| spp| yia| tmp|