International Conference on Mathematics and Computing

ICMC 2018: Mathematics and Computing pp 186-193 | Cite as

Semi-frames and Fusion Semi-frames

• Authors
• Authors and affiliations

• N. K. Sahu
• R. N. Mohapatra

Conference paper

First Online: 14 April 2018

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Part of the Communications in Computer and Information Science book series (CCIS, volume 834)

Abstract

This paper is a short survey of the theory of semi-frames and fusion semi-frames in Hilbert and Banach spaces.

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References

1. 1.
   Antoine, J.P., Balazs, P.: Frames and semi-frames. J. Phys. A Math. Theor. 44(20), 205201 (2011)MathSciNetCrossRefGoogle Scholar
2. 2.
   Casazza, P.G., Kutyniok, G.: Frames of subspaces. Contemp. Math. 345, 87–114 (2004)MathSciNetCrossRefGoogle Scholar
3. 3.
   Casazza, P.G., Christensen, O.: The reconstruction property in Banach spaces and perturbation theorem. Can. Math. Bull. 51, 348–358 (2008)MathSciNetCrossRefGoogle Scholar
4. 4.
   Christensen, O., Heil, C.: Perturbations of Banach frames and atomic decompositions. Math. Nachr. 158, 33–47 (1997)MathSciNetzbMATHGoogle Scholar
5. 5.
   Christensen, O.: An Introduction to Frames and Riesz Bases. Birkhäuser, Basel (2003)Google Scholar
6. 6.
   Daubechies, I., Grossman, A., Meyer, Y.: Painless nonorthogonal expansions. J. Math. Phys. 27, 1271–1283 (1986)MathSciNetCrossRefGoogle Scholar
7. 7.
   Duffin, R.J., Schaeffer, A.C.: A class of nonharmonic Fourier series. Trans. Am. Math. Soc. 72, 341–366 (1952)MathSciNetCrossRefGoogle Scholar
8. 8.
   Giles, J.R.: Classes of semi-inner product spaces. Trans. Am. Math. Soc. 129, 436–446 (1967)MathSciNetCrossRefGoogle Scholar
9. 9.
   Gröchenig, K.: Localization of frames, Banach frames, and the invertibility of the frame operator. J. Fourier Anal. Appl. 10, 105–132 (2004)MathSciNetCrossRefGoogle Scholar
10. 10.
    Kaushik, S.K.: A generalization of frames in Banach spaces. J. Contemp. Math. Anal. 44, 212–218 (2009)MathSciNetCrossRefGoogle Scholar
11. 11.
    Khosravi, A., Khosravi, B.: Fusion frames and G-frames in Banach spaces. Proc. Indian Acad. Sci. (Math. Sci.) 121, 155–164 (2011)MathSciNetCrossRefGoogle Scholar
12. 12.
    Koehler, D.O.: A note on some operator theory in certain semi-inner product spaces. Proc. Am. Math. Soc. 30, 363–366 (1971)MathSciNetzbMATHGoogle Scholar
13. 13.
    Lumer, G.: Semi-inner product spaces. Trans. Am. Math. Soc. 100, 29–43 (1961)MathSciNetCrossRefGoogle Scholar
14. 14.
    Sahu, N.K., Mohapatra, R.N.: Frames in semi-inner product spaces. Mathematical Analysis and its Applications. PROMS, vol. 143, pp. 149–158. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-81-322-2485-3_11CrossRefGoogle Scholar
15. 15.
    Stoeva, D.T.: On \(p\)-frames and reconstruction series in separable Banach spaces. Integral Transforms Spec. Funct. 17, 127–133 (2006)MathSciNetCrossRefGoogle Scholar
16. 16.
    Stoeva, D.T.: \(X_{d}\) frames in Banach spaces and their duals. Int. J. Pure Appl. Math. 52, 1–14 (2009)MathSciNetzbMATHGoogle Scholar
17. 17.
    Zhang, H., Zhang, J.: Frames, Riesz bases, and sampling expansions in Banach spaces via semi-inner products. Appl. Comput. Harmon. Anal. 31, 1–25 (2011)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

• N. K. Sahu
  • 1
  Email author
• R. N. Mohapatra
  • 2

1. 1.Dhirubhai Ambani Institute of Information and Communication TechnologyGandhinagarIndia
2. 2.Department of MathematicsUniversity of Central FloridaOrlandoUSA