By Hadenmalm & Zhu Borichev

ISBN-10: 0821837125

ISBN-13: 9780821837122

ISBN-10: 1641965363

ISBN-13: 9781641965361

ISBN-10: 3519914794

ISBN-13: 9783519914792

ISBN-10: 5319966016

ISBN-13: 9785319966018

This quantity grew out of a convention in honor of Boris Korenblum at the get together of his eightieth birthday, held in Barcelona, Spain, November 20-22, 2003. The booklet is of curiosity to researchers and graduate scholars operating within the conception of areas of analytic functionality, and, particularly, within the thought of Bergman areas. This booklet is copublished with Bar-Ilan collage (Ramat-Gan, Israel)

**Read or Download Bergman Spaces and Related Topics in Complex Analysis: Proceedings of a Conference in Honor of Boris Korenblum's 80th Birthday, November 20-23, 2003 PDF**

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**Additional resources for Bergman Spaces and Related Topics in Complex Analysis: Proceedings of a Conference in Honor of Boris Korenblum's 80th Birthday, November 20-23, 2003**

**Example text**

M 1:5 i:5 m, 1:5 j 5 n, Prove that for any such that if Ilzk-Ykll < 6, a A = (al ••••• a n ) zl"",zn 1:5 k :5 m, then the solution ~B = and lIa .. -b .. 1I < 6, 1J 1J of (~l""'~n) the incompatible system zl satisfies b1l\1 T ••. T b1n\n n (L i=l 53. Let in t. t1, ... ,t k Let n < k. 1 < 6, i = l, ... 1 < 6, i = l, ... ,k, then 1. 1. l. l. their least square fit polynomial Q(t) (degree < k) satisfies f/2 [f o lp(t)-Q(t)1 2 dt 5~. Let (a) < 6. e. }. a]. (b) Show that LO (c) Show that ~ is the orthogonal complement of LO' (d) For (e) Find the distances from and f E L2[-a,a] , LE are orthogonal.

9. 0), (1,1), (2,1) be given. Find the polynomial pet) of degree 1 with the least squares fit to these three points. 50. II 1 < 6. H. are linearly independent. then such that any vectors i are also linearly independent. • Yn 1, ... ,n, Hint: Consider the Gram determinant. (b) Let zl •... 'zn be linearly dependent. • yn satisfy IIZi-Yili < 6. dependent too. - .. 'Yn is linearly A .. {a , ... ,a } be a system of vectors in a Hilbert space 1 n Y E H, let YA denote the projection of y into the subspace sp{a 1 •· •• ,an}' Prove that for any e > 0, there exists a 6 > 0 such that for any system of vectors S = {bl ,··· ,bn } with the property lI a j - b j ll < 6, 1 ~ j ~ n, the Let H.

Jl 2 (n+l)(n+2). (2n+15 Thus by (3), (j)n and (4) :: (5), P ___ n_ IiPnli __1__ ~ (x 2_1)n is called the Legendre 2n n! dx n poLynomiaL of degree n. We shall refer to (j)n as the normaLized Legendre polynomial of degree n. This polynomial (j)n has the following interesting property. )2 f2"" an - (2n)! ;;;t;; = On) ! 2n+l -1 n f f 11. Orthonormal bases. Now that we know that every vector in a Hilbert space has a closest vector w in a closed subspace M, it remains to find a representation of w. It turns out that w = Lk