Functional Analysis. Inner Product spaces - Hilbert space Exercise 1: Show that (f. g) defines an inner product on the vector space E = (C'(0, 1], R)': set of all the contonous functions and their first derivatives on the closed interval (0, 1], where (Si9) = f(0)g(0) + /*s)/(1)dt %3D Hint: 'C (0, 1] = {f : [0, 1] → R, f, ƒ' e C[0, 1]}

Functional Analysis. Inner Product spaces - Hilbert space Exercise 1: Show that (f. g) defines an inner product on the vector space E = (C'(0, 1], R)': set of all the contonous functions and their first derivatives on the closed interval (0, 1], where (Si9) = f(0)g(0) + /*s)/(1)dt %3D Hint: 'C (0, 1] = {f : [0, 1] → R, f, ƒ' e C[0, 1]}

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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Functional Analysis. Inner Product spaces -
Hilbert space
Exercise 1:
Show that (f, g) defines an inner product on the vector space E = (C'(0, 1], R)': set of
all the contonous functions and their first derivatives on the closed interval (0, 1], where
(Si9) = f(0)g(0) + /* s()/(1)dt
%3D
Hint:
'C (0, 1] = {f : [0, 1] → R, f, ƒ' e C[0, 1]}

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