FRAMES, BASES AND GROUP REPRESENTATIONS Deguang Han † Department of Mathematics Texas A&M University College Station, Texas 77843 dhan@math.tamu.edu and David R. Larson ∗ Department of Mathematics Texas A&M University College Station, Texas 77843 drl3533@acs.tamu.edu 1991 Mathematics Subject Classification. Primary 46N99, 47N40, 47N99; Secondary 47D25, 47C05, 47D15, 46B28. Key words and phrases. Frame, wavelet, complementary frame, frame vector, super wavelet, frame representation. An initial version of this manuscript was dated on Dec. 1, 1996 with the title ”Frames and bases in Hilbert space”. The present version was dated on September 24, 1997 and submitted for publication. Some minor typographical and expositional corrections were made on 10/22/97. * Supported in part by NSF Grant DMS-9706810 † Participant, Workshop in Linear Analysis and Probability, Texas A&M University Typeset by A M S-T E X 1