Tikhonov Regularization and Best Approximate Inversion Formulas on Weighted Hardy Spaces

Abstract

In this paper we introduce a weighted Hardy space $\mathscr{H}_{\beta}$. This space which gives a generalization of some complex Hilbert spaces like, the Dirichlet space $\mathscr{D}$ and the Bergman space $\mathscr{A}$, it plays a background to our contribution. We use the Tikhonov regularization method and determine the extremal functions associated to the difference and primitive operators $T_{\alpha}$ and $L_{\alpha}$ on $\mathscr{H}_{\beta}$. Moreover, we deduce approximation inversion formulas for these operators.

Keywords

• Weighted Hardy space
• extremal functions
• inversion formulas

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