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Show that the Fourier transform (Using the Fourier transform on R3 with the convention shown in the first image) of the function G(x) =1/|| x || (x = (x, y, z)) is G(k)

Show that the Fourier transform (Using the Fourier transform on R3 with the convention shown in the first image) of the function G(x) =1/|| x || (x = (x, y, z)) is G(k)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.3: Algebraic Expressions
Problem 20E
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Show that the Fourier transform (Using the Fourier transform on R3 with the convention shown in the first image) of the function G(x) =1/|| x || (x = (x, y, z)) is G(k)
1 (k) (k · k)(27)³ G(k) = 47 3
Transcribed Image Text:1 (k) (k · k)(27)³ G(k) = 47 3
1 ƒ(k) = Fx->k{f(x)} = (2т)3 (27 )3 /e (x)e+ix* g³x, XER3 {(x) = Fxbx{f(k)} = / š(k)e¬ix -ix-k d³k k-x KER3
Transcribed Image Text:1 ƒ(k) = Fx->k{f(x)} = (2т)3 (27 )3 /e (x)e+ix* g³x, XER3 {(x) = Fxbx{f(k)} = / š(k)e¬ix -ix-k d³k k-x KER3
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