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【简答题】
已知函数f（x）=sin（π- ωx 2 ）cos ωx 2 +cos 2 ωx 2 - 1 2 ，（ω＞0） （1）若函数y=f（x）的周期为π，将函数y=f（x）的图象上各点的横坐标缩短为原来的 1 2 倍（纵坐标不变），再把所得的函数图象向右平移 π 8 个单位得到函数y=g（x）的图象，求y=g（x）解析式，并求其对称中心． （2）若函数y=f（x）在[ π 2 ，π]上是减函数，求ω的取值范围．
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