Cream butter and sugar together. Add corn syrup and egg yolks; beat until thoroughly blended. Stir in flour gradually. Chill dough for several hours. Beat egg whites slightly. Using 1 tablespoon of dough for each cookie, roll into balls. Brush lightly with egg white. Place two inches apart on greased cookie sheet. Bake five minutes. Remove from oven. Place a ball of Pecan Filling (below) made from 1/2 teaspoon of filling into the center of each cookie, pressing about halfway down into the cookie. Do not press completely through cookie. Return cookies to oven and bake 5 minutes longer, or until lightly browned. Cool on rack. Cookies will store for weeks if kept in a tightly closed container.