Advanced Math Question

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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E =
{u: [0, 7] → Rª | u is absolutely continuous,
le (0) = u(T). ù € L²([0, 7]. R')}
with the inner product
f′ [(ù(1), v (1)) + (u(1), v(1))]dr
for all u, v € E where (...) denotes the inner product in RN. The corresponding norm
is defined by
||lu|| £ = √² (là(1)³² + \u(1)|²)dt, V u € E.
My question is why is norm defined in
this way, please clarify
AU. VYE=
Transcribed Image Text:E = {u: [0, 7] → Rª | u is absolutely continuous, le (0) = u(T). ù € L²([0, 7]. R')} with the inner product f′ [(ù(1), v (1)) + (u(1), v(1))]dr for all u, v € E where (...) denotes the inner product in RN. The corresponding norm is defined by ||lu|| £ = √² (là(1)³² + \u(1)|²)dt, V u € E. My question is why is norm defined in this way, please clarify AU. VYE=
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