Notes on the Hawking effect in de Sitter space. I

We consider the Hawking effect for a quantized massless conformal scalar field in two- and four-dimensional de Sitter space. The relation among Bogoliubov coefficients is investigated without explicit integration of Klein-Gordon products. Our method presents a clear view of the property of Bogoliubov coefficients. In the two-dimensional case the thermal distribution is exactly derived. The application to the four-dimensional case is not straightforward, but we can derive the same result with some techniques