Reproducing Kernels And Beurlings Theorem
Reproducing Kernels And Beurlings Theorem
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Cot :?(•■; dt -3 K«;-? s-";? ba-} . ""^'O^?; "i 1>^)''. :I nii-mo'x 3ri7 "ij (i)^;; "1. ::^ •■:?* e-c . {s)^>f ';'-. "^ t^, r'", ,:S, W>I O. Jjl, . ' ■: 1 :trfe?''-avn:-ri j*. ?
\ ■■ % \ .. , ^J.^^ K-r^- ir; ir. / Ofji" V --r cJs)}r (;>, ^/ s.
s IC:^) . Od^oaii 15 We 9lao obtain, clearing of fractions In (5) ?ind differentiating: K(z, a) i-i^i^^ K(a, a) z = ^ = a (8) |o;. (a)|2 K(a, a)^ These results may be summarized as Theorem 2« The common solution (unique apart from a constant factor) of th...e extremal problems A and B Is '^ (z) = i-'-'^(2), lAjhich is uniquely determined from the formulas (5), (6) once arg vj (y, ) is given at some point. The maximum in problem A is the right side of (6), the maximum in problem 3 is the right side^ of (8).
3. 3 Let us nov consider a generalization of problem A: Problem A « e B, W 0\\ ^ ± ^ » ^(a^) = ... ^(a^) = . Maximize |0(^)|« Here a. , ... A are distinct points of -^ i. • Denote by S the closed (invariant) subsp^ce of H consisting of all functions vanishing at a^, ••• a » Let k (z, ^) denote.
What to read after Reproducing Kernels And Beurlings Theorem?
You can find similar books in the "Read Also" column, or choose other free books by Harold S Shapiro to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Cot :?(•■; dt -3 K«;-? s-";? ba-} . ""^'O^?; "i 1>^)''. :I nii-mo'x 3ri7 "ij (i)^;; "1. ::^ •■:?* e-c . {s)^>f ';'-. "^ t^, r'", ,:S, W>I O. Jjl, . ' ■: 1 :trfe?''-avn:-ri j*. ?
\ ■■ % \ .. , ^J.^^ K-r^- ir; ir. / Ofji" V --r cJs)}r (;>, ^/ s.
s IC:^) . Od^oaii 15 We 9lao obtain, clearing of fractions In (5) ?ind differentiating: K(z, a) i-i^i^^ K(a, a) z = ^ = a (8) |o;. (a)|2 K(a, a)^ These results may be summarized as Theorem 2« The common solution (unique apart from a constant factor) of th...e extremal problems A and B Is '^ (z) = i-'-'^(2), lAjhich is uniquely determined from the formulas (5), (6) once arg vj (y, ) is given at some point. The maximum in problem A is the right side of (6), the maximum in problem 3 is the right side^ of (8).
3. 3 Let us nov consider a generalization of problem A: Problem A « e B, W 0\\ ^ ± ^ » ^(a^) = ... ^(a^) = . Maximize |0(^)|« Here a. , ... A are distinct points of -^ i. • Denote by S the closed (invariant) subsp^ce of H consisting of all functions vanishing at a^, ••• a » Let k (z, ^) denote.
What to read after Reproducing Kernels And Beurlings Theorem?
You can find similar books in the "Read Also" column, or choose other free books by Harold S Shapiro to read onlineMoreLess
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