(1) Consider the Gaussian kernel of the form 1 p(x,t) = V2nt Show that p(x, 0+) = 8(x). Remark 0.1. Here p(x,0+) 9 lim-→0 P(x, t) and 8(x) is Dirac concentrated at 0. def
(1) Consider the Gaussian kernel of the form 1 p(x,t) = V2nt Show that p(x, 0+) = 8(x). Remark 0.1. Here p(x,0+) 9 lim-→0 P(x, t) and 8(x) is Dirac concentrated at 0. def
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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Transcribed Image Text:(1) Consider the Gaussian kernel of the form
1
p(x, t) =
V2nt
2t
Show that
p(x,0+) = 8(x).
Remark 0.1. Here p(x,0+)
def
limt-→0 P(x, t) and 8(x) is Dirac concentrated at 0.
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