▁Pos itive - defin ite ▁function ▁on ▁a ▁group ▁ ▁Character istic ▁function ▁( prob ability ▁theory ) ▁ ▁References ▁▁ ▁M . ▁Re ed ▁and ▁Barry ▁Simon , ▁Method s ▁of ▁Modern ▁Mathemat ical ▁Physics , ▁vol . ▁II , ▁Academ ic ▁Press , ▁ 1 9 7 5 . ▁ ▁Category : The or ems ▁in ▁harm onic ▁analysis ▁Category : The or ems ▁in ▁measure ▁theory ▁Category : The or ems ▁in ▁functional ▁analysis ▁Category : The or ems ▁in ▁Fourier ▁analysis ▁Category : Stat ist ical ▁the or ems <0x0A> </s> ▁The ▁Chap el ▁of ▁St . ▁Paul ▁is ▁a ▁Roman ▁Catholic ▁parish ▁church ▁under ▁the ▁authority ▁of ▁the ▁Roman ▁Catholic ▁Arch di oc ese ▁of ▁New ▁York , ▁located ▁in ▁Staats burg , ▁Dutch ess ▁County , ▁New ▁York . ▁It ▁was ▁established ▁in ▁ 1 8 8 7 . ▁It ▁is ▁a ▁mission ▁chap el ▁of ▁Church ▁of ▁Regin a ▁Co eli ▁in ▁Hy de ▁Park . ▁ ▁History ▁The ▁first ▁Roman ▁Catholic ▁church ▁in ▁Staats burgh ▁was ▁a ▁stone ▁structure ▁built ▁in ▁ 1 8 4 9 ▁by ▁Rev . ▁Michael ▁J . ▁Ri ord an , ▁past or ▁of ▁St . ▁Peter ' s , ▁P ough ke eps ie , ▁on ▁Clay ▁Hill , ▁on ▁land ▁owned ▁by ▁William ▁Em m ett , ▁cousin ▁of ▁New ▁York ▁Att orney ▁General ▁Thomas ▁Add is ▁Em met . ▁ ▁It ▁was ▁served ▁but ▁Father ▁August ine ▁P . ▁Anderson , ▁O . P ., ▁who ▁also