Reference no: EM13990808
1. Let fnk (x ) := ank for 2k ≤ 2n x < >2k + 1 and fnk (x ) = bnk for 2k + 1 ≤ x 2k + 2, for each n = 0, 1,... and k = 0, 1,..., K (n). Find values of K (n), ank , and bnk such that the set of all the functions fnk is an orthonormal basis of L2([0, 1], λ). How uniquely are ank and bnk determined?
2. Let (X, S, µ) and (Y, T , ν) be two measure spaces. Let { fn } be an orthonormal basis of L2(X, S, µ) and {gn } an orthonormal basis of L2(Y, T , ν). Show that the set of all functions hmn (x, y) := fm (x )gn (y) is an orthonormal basis of L2(X × Y, S ⊗ T ,µ × ν).
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What is the object acceleration
: Three forces. one of 40.0 N directed due north, the second of 65.0 N due east and a third of 100 N at 35.0 degrees west of south act on an object of 15.0 kg. What is the object's acceleration?
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Problem regarding the hahn decomposition theorem
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Conclusion of the radon-nikodym theorem
: In [0, 1] with Borel σ-algebra B, let µ( A) = 0 for all A ∈ B of first cate- gory and µ( A) = +∞ for all other A ∈ B. Show that µ is a measure, and that if ν is a finite measure on B absolutely continuous with respect to µ, then ν ≡ 0. Hint: See §..
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Continuous with respect to counting measure
: Lebesgue measure λ is absolutely continuous with respect to counting measure c on [0, 1], which is not σ-finite. Show that the conclusion of the Radon-Nikodym theorem does not hold in this case (there is no "derivative" dλ/dc having the properties..
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Problem regarding the orthonormal basis
: Let (X, S, µ) and (Y, T , ν) be two measure spaces. Let { fn } be an orthonormal basis of L2(X, S, µ) and {gn } an orthonormal basis of L2(Y, T , ν). Show that the set of all functions hmn (x, y) := fm (x )gn (y) is an orthonormal basis of L2(X × ..
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Discuss and predict the outcomes with the use of panel data
: The reading for this module discusses panel data and the use of pooled cross-sectional analysis. Post a research question you would be interested in pursuing. Then discuss and predict the outcomes with the use of panel data and the use of pooled c..
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Prepare necessary adjusting entries for month of september
: On September 30, Sweet Cheeks completed service for which it had received payment in August, $1,500. Prepare all necessary adjusting entries for the month of September.
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Unique nonnegative radon measure
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Project breakdown risks and staffing
: Project Breakdown, Risks and Staffing - PMI is one of the world's largest not-for-profit membership associations for the project management profession
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