(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.

Linear Algebra: A Modern Introduction
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ISBN:9781285463247
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Chapter7: Distance And Approximation
Section7.4: The Singular Value Decomposition
Problem 51EQ
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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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