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Consider the Volterra integration operator V: L2 ([0,1])→ L² ([0,1]) defined by (V f)(x) = f f(t) dt, for every fEL2 ([0,1]). Find the polar decomposition of V

Consider the Volterra integration operator V: L2 ([0,1])→ L² ([0,1]) defined by (V f)(x) = f f(t) dt, for every fEL2 ([0,1]). Find the polar decomposition of V

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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Consider the Volterra integration operator V: L2 ([0, 1])→ L2 ([0,1]) defined by (V f)(x) = f(t) dt, for every fEL² ([0,1]). Find the polar decomposition of V
Transcribed Image Text:Consider the Volterra integration operator V: L2 ([0, 1])→ L2 ([0,1]) defined by (V f)(x) = f(t) dt, for every fEL² ([0,1]). Find the polar decomposition of V
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