Abstract:For a class of analytic functions in a bounded convex domain $G$ that admit an exponential series expansion in $D$, the behavior of the coefficients of this expansion is studied in terms of the growth order near the boundary $\partial G$. In the case where $G$ has a smooth boundary, unimprovable two-sided estimates are established for the order via characteristics depending only on the exponents of the exponential series and the support function of $G$. As a consequence, a formula is obtained for the growth of the exponential series via the coefficients and the support function of the convergence domain $G$.

---

中文翻译：

---

收敛域边界附近指数级数的增长阶数

摘要：对于在有界凸域 $G$ 中允许在 $D$ 中进行指数级数展开的一类解析函数，根据边界 $\partial G 附近的增长顺序来研究这种展开的系数的行为。美元。在 $G$ 具有平滑边界的情况下，仅依赖于指数级数的指数和 $G$ 的支持函数，为通过特征建立不可改进的双边估计。因此，通过收敛域$G$的系数和支持函数，得到了指数级数增长的公式。

---