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Studia Scientiarum Mathematicarum Hungarica
Authors:
Chuanyi Zhang
and
Chenhui Meng
To answer a question in [24], we propose \documentclass{aastex}
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\DeclareMathSizes{10}{9}{7}{6}
\begin{document}
$$\mathcal{U}\mathcal{L}\mathcal{P}(\mathbb{R}^ + ,H)$$
\end{document} , the space of uniform limit power functions and \documentclass{aastex}
\usepackage{amsbsy}
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\DeclareMathSizes{10}{9}{7}{6}
\begin{document}
$$\mathcal{L}\mathcal{P}_2$$
\end{document} , the space of limit power functions. We show that \documentclass{aastex}
\usepackage{amsbsy}
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\usepackage{stmaryrd}
\usepackage{textcomp}
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\usepackage{portland,xspace}
\usepackage{amsmath,amsxtra}
\usepackage{bbm}
\pagestyle{empty}
\DeclareMathSizes{10}{9}{7}{6}
\begin{document}
$$\mathcal{U}\mathcal{L}\mathcal{P}(\mathbb{R}^ + ,H)$$
\end{document} and \documentclass{aastex}
\usepackage{amsbsy}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{bm}
\usepackage{mathrsfs}
\usepackage{pifont}
\usepackage{stmaryrd}
\usepackage{textcomp}
\usepackage{upgreek}
\usepackage{portland,xspace}
\usepackage{amsmath,amsxtra}
\usepackage{bbm}
\pagestyle{empty}
\DeclareMathSizes{10}{9}{7}{6}
\begin{document}
$$\mathcal{L}\mathcal{P}_2$$
\end{document} have properties respectively similar to that of \documentclass{aastex}
\usepackage{amsbsy}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{bm}
\usepackage{mathrsfs}
\usepackage{pifont}
\usepackage{stmaryrd}
\usepackage{textcomp}
\usepackage{upgreek}
\usepackage{portland,xspace}
\usepackage{amsmath,amsxtra}
\usepackage{bbm}
\pagestyle{empty}
\DeclareMathSizes{10}{9}{7}{6}
\begin{document}
$$\mathcal{A}\mathcal{P}(\mathbb{R}^ + ,H)$$
\end{document} , the space of almost periodic functions and to that of
B
2
, Besicovitch’s space. Finally, we point out that \documentclass{aastex}
\usepackage{amsbsy}
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\usepackage{portland,xspace}
\usepackage{amsmath,amsxtra}
\usepackage{bbm}
\pagestyle{empty}
\DeclareMathSizes{10}{9}{7}{6}
\begin{document}
$$\mathcal{L}\mathcal{P}_2$$
\end{document} is the largest among those Hilbert spaces in limit power function set whose members have associated Fourier series (in the sense of a new basis) and satisfy Parseval’s equality.
