What were the apostles trying to convince the nation of Israel about Jesus?

Les explains that after the Holy Spirit came upon them, the apostles received miracle-working power and were to be witnesses in Jerusalem, Judea, Samaria, and unto most parts of the earth. They were an extension of Christ's earthly ministry: what Jesus and the twelve had performed in those three years, Peter and the eleven were to continue, because they were dealing with the same people—the nation of Israel. They were trying to convince the nation that Jesus was who He said He was, and that He was still going to fulfill His promises if they would simply believe. They continued with signs and wonders, gathered with one accord in Solomon's Porch at the Temple, not having stopped sacrifices or Judaistic ritual; the only addition was believing that Jesus was whom He said He was. Les also notes that archaeologists are finding evidence of first- and second-century Jews who practiced Judaism while embracing Jesus of Nazareth as Messiah.