Applied Analysis Errata II

Applied Analysis Errata II - Errata Applied Analysis...

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Unformatted text preview: Errata Applied Analysis (Corrected in online files but not in Second Printing) • p. 115: Replace statement of Theorem 5.53 with: “A consistent approximation scheme is convergent if and only if it is stable.” • p.115: Replace last paragraph (“Conversely...”) of the proof of Theorem 5.53 with: “Conversely, we prove that a convergent scheme is stable. For any f ∈ Y , let u = A−1 f . Then, since the scheme is convergent, we have u → u as → 0, where u = A−1 f , so that u is bounded. Thus, there exists a constant Mf , independent of , such that A−1 f ≤ Mf . The uniform boundedness theorem, which we do not prove here, then implies that there exists a constant M such that A−1 ≤ M , so the scheme is stable.” • p. 213, Exercise 8.14: Replace last sentence by: “Use a polarizationtype identity to prove that if H is a complex Hilbert space and x, Ax = x, Bx for all x ∈ H, then A = B . What can you say about A and B for real Hilbert spaces?” • p. 239, Exercise 9.3: “Suppose that A is a bounded linear operator on a...” • p. 362, “...1/x belongs to...” • p. 427 “Dautry” should be “Dautray”. • p. 428 “Mallet” should be “Mallat”. ...
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This note was uploaded on 03/23/2012 for the course AMATH 567 taught by Professor A.g during the Fall '11 term at University of Washington.

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