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- W2556616009 abstract "Given a finite set sigma of the unit disc mathbb{D}={zinmathbb{C}:,,vert zvert 0 for every kgeq0 and overline{lim}_{k}(1/w_{k}^{1/k})=,1, and for the corresponding interpolation constant cleft(sigma,, X,, H^{infty}right), we show that if p=2, cleft(sigma,, X,, H^{infty}right)leq avarphi_{X}left(1-frac{1-r}{n}right) where n=#sigma, r=max_{lambdainsigma}left|lambdaright| and where varphi_{X}(t) stands for the norm of the evaluation functional fmapsto f(t) on the space X. The upper bound is sharp over sets sigma with given n and r. For X=l_{a}^{p}(w_{k}), pneq2 and X=L_{a}^{p}left(left(1-left|zright|^{2}right)^{beta}dxdyright) (the weighted Bergman space), beta>-1, 1leq p<2, we also found upper and lower bounds for cleft(sigma,, X,, H^{infty}right) (sometimes for special sets sigma) but with some gaps between these bounds." @default.
- W2556616009 created "2016-11-30" @default.
- W2556616009 creator A5016748336 @default.
- W2556616009 date "2008-01-01" @default.
- W2556616009 modified "2023-09-27" @default.
- W2556616009 title "Constrained Nevanlinna-Pick interpolation in Weighted Hardy and Bergman spaces" @default.
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