Unformatted text preview: b) Show that I is a bounded operator, that is, there exists a number B so that k If k ∞ ≤ B k f k ∞ for all f ∈ C [0 , 2] and find the (smallest) number B . 3. Consider the differentiation operator D : P → P (acting on polyno-mials): Df = df dt a) Show that D is a linear transformation. b) Equip P with the sup norm on [0 , 2]. Show that D is an unbounded operator: consider the polynomials f n ( t ) = t n and show that there is no constant B so that k Df n k ∞ ≤ B k f n k ∞ for all n . 1...
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- Winter '08
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- Linear Algebra, Algebra, Derivative, Inequalities, Continuous function, limit limn→∞ fn
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