In this thesis, we introduce and study spaces to obtain multiresolution analysis(which will be abbreviated ”MRA”). The idea of MRA was developed in 1986 by Mallat and Meyer. In recent years, the concept of MRA has become an important tool in matematics and applications. It rovides a natural framework for understanding of wavelet bases, ases that consist of the scaled and integer translated versions of a finite number of functions, and the construction of new examples. The theory of MRA has its roots in image and multiscale signal processing, and it is concerned with the decomposition of signals into suaces of different resolutions. If we think of the core suace as a specified level of resolution, then moving to amounts to” zooming in” and incerasing resolution by one level. On the other hand, represents one lower level of resolution, resulting from ”zooming out”. Working on MRA in the setting of LCA groups is a challenging task, but it turns out to be useful, since it determines the basic features of MRA and includes most of the special cases. Dahlke generalized the definition of MRA to LCA groups. In fact he showed that under certain conditions the generalized B-splines generate an MRA. MRA in - space on locally compact abelian group is one of fundemental concept of wavelet theory. For any integers we determine function ? in which