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E = {u: [0, 7] - RNu is absolutely continuous. uz (0) = u(7). ù e L²([0. 7]. RN)) with the inner product - f′ (cù(1), v(1)) + (u(1), v(1))]dr AU. VYEM for all u, v € E where (-.-) denotes the inner product in RN. The corresponding norm is defined by

E = {u: [0, 7] - RNu is absolutely continuous. uz (0) = u(7). ù e L²([0. 7]. RN)) with the inner product - f′ (cù(1), v(1)) + (u(1), v(1))]dr AU. VYEM for all u, v € E where (-.-) denotes the inner product in RN. The corresponding norm is defined by

Advanced Engineering Mathematics
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 = { [0, 7] RNu is absolutely continuous. le (0) = u(T). ù L²([0. 7]. RN)) with the inner product - <<U. VYE= • f*((ú(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 Helle = + \u()dr, Vus E. My question is why is norm defined in this way, please clarify
Transcribed Image Text:E = { [0, 7] RNu is absolutely continuous. le (0) = u(T). ù L²([0. 7]. RN)) with the inner product - <<U. VYE= • f*((ú(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 Helle = + \u()dr, Vus E. My question is why is norm defined in this way, please clarify
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