From Acts of the Apostles, by William S. Kurz, SJ, commenting on Acts 10:34a, 37-43
Peter’s sermon reaches its climax with the early Christian creedal statement “This man God raised [on] the third day.” As confirmation of Jesus’ resurrection, Peter focuses not on the empty tomb but on the testimony of us, the witnesses chosen by God in advance. He testifies that Jesus did not appear to all the people, but to us only. The risen Jesus will not be seen by his enemies or unbelievers, nor even by the vast majority of followers, until his return at the end of the world, when “they will see the Son of Man coming in a cloud with power and great glory” (Luke 21:27). Until then, “we walk by faith, not by sight” (2 Cor 5:7).
Peter declares that Jesus commissioned us to preach to the people and testify to him. This speech to Gentiles differs from Peter’s earlier speech to Jews, where he had cited the resurrection to argue, “Therefore let the whole house of Israel know for certain that God has made him both Lord and Messiah” (Acts 2:36). To Gentiles, who would not be familiar with Jewish messianic prophecies, he cites the fact of the resurrection to argue that Jesus is the one appointed by God as judge of the living and the dead. Paul’s speech to the Athenians will similarly refer to the risen Jesus as universal judge on the last day (Acts 17:31).
Christian belief in the risen Jesus is also grounded in all the prophets of the Old Testament, who bear witness to Jesus. That is, faith in the resurrection is based on both the living witness of apostles who saw Jesus risen and on the Old Testament prophecies. The aim of both the testimony of eyewitnesses and the prophecies is that every believer in Jesus will receive forgiveness of sins through his name. The essence of salvation is that people’s sins are forgiven by invoking Jesus’ name, because of all that he has accomplished on their behalf.