2. Let 2 be an open set in R" with n ≥ 3, and u be a harmonic function in N. Let & € Rn and> > 0. Define1²(x-E)X|x - §|n-2u‹,x(x):Prove that αξ,λ is harmonic in its domain.=-Uε +

Given: Ω is an open set in ℝn with n≥3. u is a harmonic function in Ω. ξ∈ℝn and λ>0 uξ,λ(x)…

2. Let 2 be an open set in R" with n ≥ 3, and u be a harmonic function in N. Let & € R¹ and A> 0. Define Prove that αξ,λ u૬,A(T) := := 1 |x - ε|n-20 u (ε + № ²(x=0)). - 5/1²). is harmonic in its domain.

2. Let 2 be an open set in R" with n ≥ 3, and u be a harmonic function in N. Let & € R¹ and A> 0. Define Prove that αξ,λ u૬,A(T) := := 1 |x - ε|n-20 u (ε + № ²(x=0)). - 5/1²). is harmonic in its domain.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.5: The Kernel And Range Of A Linear Transformation

Problem 10EQ

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Question

2. Let 2 be an open set in R" with n ≥ 3, and u be a harmonic function in N. Let & € Rn and
> > 0. Define
1²(x-E)
X
|x - §|n-2
u‹,x(x):
Prove that αξ,λ is harmonic in its domain.
=
-U
ε +

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