En(x,y) be a basic solution of the Laplace equation. and x is fixed point in R^n. Let L() be the distribution (on the Schwartz space) corresponding to the function En(x,*) །།། ། ་་ Find all distributions (on the Schwartz space) Z that satisfy the equation (AL() = x(): AZ(·) — 4Z(·) = ½-½³x(·) — 2L(·), where delta(x) is the Dirac delta at point x (reminder delta(x) = DELTA(L())

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Differential equations: anyone here who can solve this pde correctly and handwritten plz
En(x,y) be a basic solution of the Laplace equation. and x is fixed point in R^n.
Let L() be the distribution (on the Schwartz space) corresponding to the function En(x,*)
།།། ། ་་
Find all distributions (on the Schwartz space) Z that satisfy the equation
(AL() = x():
AZ(·) — 4Z(·) = ½-½³x(·) — 2L(·),
where delta(x) is the Dirac delta at point x (reminder delta(x) = DELTA(L())
Transcribed Image Text:En(x,y) be a basic solution of the Laplace equation. and x is fixed point in R^n. Let L() be the distribution (on the Schwartz space) corresponding to the function En(x,*) །།། ། ་་ Find all distributions (on the Schwartz space) Z that satisfy the equation (AL() = x(): AZ(·) — 4Z(·) = ½-½³x(·) — 2L(·), where delta(x) is the Dirac delta at point x (reminder delta(x) = DELTA(L())
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