University of MaraghehSahand Communications in Mathematical Analysis2322-580704120161101Construction of continuous $g$-frames and continuous fusion frames435522217ENMahdiyeh KhayyamiDepartment of Mathematics, Science and Research Branch, Islamic Azad University, Kerman, Iran.Akbar NazariDepartment of Mathematics, Science and Research Branch, Islamic Azad University, Kerman, Iran.Journal Article20151224A generalization of the known results in fusion frames and $g$-frames theory to continuous fusion frames which defined by M. H. Faroughi and R. Ahmadi, is presented in this study. Continuous resolution of the identity (CRI) is introduced, a new family of CRI is constructed, and a number of reconstruction formulas are obtained. Also, new results are given on the duality of continuous fusion frames in Hilbert spaces.http://scma.maragheh.ac.ir/article_22217_ae4c4518ab8f84876feb316820fad8b5.pdf