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(2) Show that if f has support in a compact set A CR and g has support in a compact set B C R then f * g has support in A+ B := {r+ y : x € A, y e B}. f*g is convolution.

(2) Show that if f has support in a compact set A CR and g has support in a compact set B C R then f * g has support in A+ B := {r+ y : x € A, y e B}. f*g is convolution.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please explain step by step, and show details clearly. Thanks In this problem set define the Fourier transform of a function f € L'(R) by (2) Show that if f has support in a compact set A CR and g has support in a compact set BCR then f *g has support in A + B := {r+ y : x € A, y € B}. f*g is convolution.
Transcribed Image Text:Please explain step by step, and show details clearly. Thanks In this problem set define the Fourier transform of a function f € L'(R) by (2) Show that if f has support in a compact set A CR and g has support in a compact set BCR then f *g has support in A + B := {r+ y : x € A, y € B}. f*g is convolution.
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