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Aeejq h lxg u. And x = (xk), then Penx = xnen Example 810 If H = L2(T) is the space of 2ˇperiodic functions and u = 1= p 2ˇ is the constant function with norm one, then the orthogonal projection Pu maps a function to its mean Puf = hfi, where hfi = 1 2ˇ Z2ˇ 0 f(x)dx The corresponding orthogonal decomposition, f(x) = hfi f0(x. @ L X g ` M 򂷂 l X ́A A J 암 ɑ B ȑO ͓암 ɂ͖ } x l X A P X V O N 㔼 L X g ` ȂǕێ n ̋ Ƌ a } т ߂ ʁA a } x A } ɑ΂ x ͌ B ̂Ƃ A 암 ̐l X ̑ ̓u b V x Ă 邪 A H ̑I Ɍ Ė } ̃P ₪ C X G ̑΃A u Ό p A C N ̒ A 搧 U Ȃǂ x ̂́A L X g ` ̗L ҂ 荞 ݁A 암 a } D ҂ ړI ̂ Ȃ B i"A look at America's polarized electorate" j. H(u,α) I Figure 1 The set I Proposition 61 If X is a convex set, and f ·),g1(·),,g m(·) are convex functions on X, then I is a convex set 13 Let H u,α = {(s,z) ∈ IR m1 u sT z = α} We call H u,α is a lower support of I if uT s z ≥ α for all (s,z) ∈ I Let L = {(s,z) ∈ IR m1 s =0} Note that H u,α ∩ L = {(0,α)} The problem of determining a hyperplane H u,α th.

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Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, history. Все языки доступны здесь Q L H W L H ?. Notice that if uh is a solution to the homogeneous equation (19), and upis a particular solution to the inhomogeneous equation (111), then uhupis also a solution to the inhomogeneous equation (111) Indeed L(uh up) = Luh Lup= 0 g= g Thus, in order to nd the general solution of the inhomogeneous equation (111), it is enough to nd the general solution of the homogeneous.

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