Abstract：Based on the frame theorem of Hilbert spaces,a large number of continuous generalized frames are constructed from existing continuous generalized frames by adopting operator methods.Moreover,a necessary and sufficient condition for the finite sum of continuous generalized frames to be a continuous generalized frame is obtained.The results provide new methods to construct continuous generalized frames.
1 GABOR D.Theory of communications［J］.Journal of the Institution of Electrical Engineers，1946，93：429-457. 2 DUFFIN R J，SHAFFER A C.A class of nonharmonic Fourier series［J］.Transactions of the American Mathematical Society，1952，72（2）：341-366. 3 DAUBECHIES I，GROSSMANN A，MEYER Y.Painless nonorthogonal expansions［J］.Journal of Mathematical Physics，1986，27（5）：1271-1283. 4 CHRISTENSEN O. An Introduction to Frames and Riesz Bases［M］. Boston：Birkh?user，2016. 5 ABDOLLAHPOUR M R，KHEDMATI Y.On some properties of continuous g-frames and Riesz-type continuous g-frames［J］.Indian Journal of Pure & Applied Mathematics，2016，48（1）：1-16. DOI：10.1007/s13226-016-0208-1 6 肖祥春，曾晓明.连续g-框架的刻画［J］.数学学报（中文版），2012，55（6）：1131-1144. XIAO X C，ZENG X M.Characterization of continuous g-frames［J］.Acta Mathematica Sinica（Chinese Series），2012，55（6）：1131-1144. 7 ALI S T，ANTOINE J P，GAZEAU J P. Continuous frames in Hilbert spaces［J］.Annals of Physics，1992，222（1）：1-37. DOI：10.1088/1751-8113/45/24/24 4023 8 SUN W C. g-frames and g-Riesz bases［J］. Journal of Mathematical Analysis & Applications，2006，322（1）：437-452. DOI：10.1016/j.jmaa.2005.09.039 9 ABDOLLAHPOUR M R，FAROUGHI M H.Continuous g-frames in Hilbert spaces［J］.Southeast Asian Bulletin of Mathematics，2008，32（1）：1-19. 10 OBEIDAT S，SAMARAH S，CASAZZA P G，et al.Sums of Hilbert space frames［J］.Journal of Mathematical Analysis and Applications，2016，351（2）：579-585. DOI：10.1016/j.jmaa.2008.10.040
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