Λεπτομέρειες βιβλιογραφικής εγγραφής
| Τίτλος: |
Approximate Taylor Theorem for Analytic Lipschitz Functions. |
| Συγγραφείς: |
Deterding, Stephen1 (AUTHOR) deterding@marshall.edu |
| Πηγή: |
Constructive Approximation. May2026, p1-12. 12p. |
| Θεματικοί όροι: |
*Taylor's series, *Lipschitz spaces, *Analytic functions, *Mathematical complex analysis |
| Περίληψη: |
Let U be a bounded open subset of the complex plane and let Aα(U)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$A_{\alpha }(U)$$\end{document} denote the set of functions analytic on U that also belong to the little Lipschitz class with Lipschitz exponent α\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\alpha $$\end{document}. It is shown that if Aα(U)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$A_{\alpha }(U)$$\end{document} admits a bounded point derivation at x∈∂U\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$x \in \partial U$$\end{document}, then there is an approximate Taylor Theorem for Aα(U)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$A_{\alpha }(U)$$\end{document} at x. This extends and generalizes known results concerning bounded point derivations. [ABSTRACT FROM AUTHOR] |
| Βάση Δεδομένων: |
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