mega ,0}+\sum _{k=h+1}^{0} 2^{k-1}\beta ^\delta _{\omega ,k}(U,{\vec {\tau }}_h,\ldots ,{\vec {\tau }}_0)\big )\;, \end{aligned}$$\end{document}$$with the understanding that $\documentclass[12pt]{minimal}
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                \begin{document}$$\xi _{+,h}=\delta _{+,h}=0$$\end{document}$, $\documentclass[12pt]{minimal}
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                \begin{document}$$\forall h<h^*_1$$\end{document}$. Consider first the case $\documentclass[12pt]{minimal}
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                \begin{document}$$\omega =-$$\end{document}$. By imposing the condition that $\documentclass[12pt]{minimal}
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                \begin{document}$$\xi _{-,h^*_2}=\delta _{-,h^*_2}=0$$\end{document}$, we find that$$\documentclass[12pt]{minimal}
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                \usepackage{