Double-sided Taylor's approximations and their applications in theory of trigonometric inequalities

Double-sided Taylor's approximations and their applications in Theory of analytic inequalities

In this paper the double-sided Taylor's approximations are studied. A short proof of a well-known theorem on the double-sided Taylor's approximations is introduced. Also, two new theorems are proved regarding the monotonicity of such approximations. Then we present some new applications of the double-sided Taylor's approximations in the theory of analytic inequalities.

雅可比与三角Dunkl热核的精确估计

Sharp estimates for the Jacobi and trigonometric Dunkl heat kernels

该研究针对秩1情形的W-不变三角Dunkl热核（含根系A₁、BC₁）证明精确双边估计，进而得到全范围类型参数下非紧雅可比热核的精确界。