1. Consider real Sobolev space W².1[–1, 1] and functional f(x) = Ltx(t)dt. Find z E W².1 such that Va E W2.[-1, 1], f(x) = (x, 2). Remark: Space W².1 has inner product (x, y) = S(xy+x'y')dt.
1. Consider real Sobolev space W².1[–1, 1] and functional f(x) = Ltx(t)dt. Find z E W².1 such that Va E W2.[-1, 1], f(x) = (x, 2). Remark: Space W².1 has inner product (x, y) = S(xy+x'y')dt.
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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![1. Consider real Sobolev space W².'[–1, 1] and functional f(x) = L, tx(t)dt. Find z E W2.1 such
that Vr E W².1[-1,1], ƒ(x) = (x, z).
Remark: Space W2.1 has inner product (x, y) = [(xy+x'y')dt.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F98fd4674-b7c0-4400-9a5b-dee54faaab3f%2F74160482-45cc-4a25-9fdd-a932cef3498b%2Fg1t9pyb_processed.png&w=3840&q=75)
Transcribed Image Text:1. Consider real Sobolev space W².'[–1, 1] and functional f(x) = L, tx(t)dt. Find z E W2.1 such
that Vr E W².1[-1,1], ƒ(x) = (x, z).
Remark: Space W2.1 has inner product (x, y) = [(xy+x'y')dt.
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