A NECESSARY AND SUFFICIENT CONDITION FOR THE BIORTHOGONALITY OF {1,2}

1.IntroductionLetRbethecollectionofallrealnumbers,andZthecollectionofallintegers.Iff1(x)andf2(x)aretwofunctionsinL2(R),theinnerproductisgivenbyWesayf1(x)andf2(x)arebiorthogonal,ifFirstletusdescribeaclassoffunctions(x)and(2)inL2(R)asfollows.Thr...