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Let be a function.Which of the following descriptive statements regarding its Fourier transformare correct? I. The Fourier transform converts differentiation in into multiplication in.II. The smoothness of is closely related to the asymptotic decay rate of its Fourier transform?III. The asymptotic decay rate of determines the smoothness of its Fourier transform.

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MCQs on Partial Differential Equations.


Let<br><img src='https://www.fatskills.com/images2/GradExams/B947294D-D0CC-4B38-8A0B-6B76B4122DE5.png' height='20' width='35'/> be a function.Which of the following descriptive statements regarding its Fourier transform<br><img src='https://www.fatskills.com/images2/GradExams/A81F4CB6-0452-44D8-AE7C-AFCA8896C67A.png' height='25' width='36'/>are correct?<br/> I. The Fourier transform converts differentiation in<br><img src='https://www.fatskills.com/images2/GradExams/89FD89E4-C10B-4D08-9EE0-9D8541E9437A.png' height='10' width='11'/> into multiplication in<br><img src='https://www.fatskills.com/images2/GradExams/F7B619CA-9D69-48F4-9024-E0902F2B5AA0.png' height='10' width='11'/>.<br/>II. The smoothness of<br><img src='https://www.fatskills.com/images2/GradExams/203085BB-4CDE-402E-A5EC-575C34B85EBF.png' height='18' width='10'/> is closely related to the asymptotic decay rate of its Fourier transform<br><img src='https://www.fatskills.com/images2/GradExams/02A2E72B-F2D6-4F41-9AD5-8370FC0F5AFF.png' height='24' width='11'/>?<br/>III. The asymptotic decay rate of<br><img src='https://www.fatskills.com/images2/GradExams/203085BB-4CDE-402E-A5EC-575C34B85EBF.png' height='18' width='10'/> determines the smoothness of its Fourier transform.






 
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