Let CR be the space of all continuous and bounded functions x(t) on R with norm ||x|| = supR |x(t)|. On the space CR we define the operator A by (Ax) (t) = x(t+c), where c ER is a constant. Prove that o(A) = {λ € C : |\| = 1}.
Let CR be the space of all continuous and bounded functions x(t) on R with norm ||x|| = supR |x(t)|. On the space CR we define the operator A by (Ax) (t) = x(t+c), where c ER is a constant. Prove that o(A) = {λ € C : |\| = 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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