Let V = C([−π, π]) be the space of continuous real-valued functions on the closed interval [−^,^], and endow V with the inner product (f,g) = f(x)g(x) dx. Show that the subset {1, cos(x), sin(x), cos(2x), sin(2x), ...} of V is orthogonal, and normalize it to obtain an orthonormal subset of V.
Let V = C([−π, π]) be the space of continuous real-valued functions on the closed interval [−^,^], and endow V with the inner product (f,g) = f(x)g(x) dx. Show that the subset {1, cos(x), sin(x), cos(2x), sin(2x), ...} of V is orthogonal, and normalize it to obtain an orthonormal subset of V.
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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![2. Let V = C([-T, π]) be the space of continuous real-valued functions on the closed
Sf(x)g(x) dx.
interval [—π, π], and endow V with the inner product (f,g)
Show that the subset {1, cos(x), sin(x), cos(2x), sin(2x),...} of V is orthogonal, and
normalize it to obtain an orthonormal subset of V.
=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff2e948f6-fd6f-485f-942e-c931230f8579%2F78af4159-b456-4e5b-b50a-011fd98bd080%2Faj5n9jr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Let V = C([-T, π]) be the space of continuous real-valued functions on the closed
Sf(x)g(x) dx.
interval [—π, π], and endow V with the inner product (f,g)
Show that the subset {1, cos(x), sin(x), cos(2x), sin(2x),...} of V is orthogonal, and
normalize it to obtain an orthonormal subset of V.
=
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