On Weighted Banach Frames

Authors

  • L. K. Vashisht Department of Mathematics, University of Delhi, Delhi 110007
  • Shalu Sharma Department of Mathematics, University of Delhi, Delhi 110007

DOI:

https://doi.org/10.26713/cma.v3i3.212

Keywords:

Frames, Banach frames

Abstract

We introduce and study weighted Banach frames in Banach spaces. Necessary and/or sufficient conditions for a weighted Banach frame to be exact are given. An application of weighted Banach frames is discussed.

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References

P.G. Casazza, The art of frame theory,Taiwanese J. Math.4(2) (2000), 129–201.

P.G. Casazza, D. Han and D.R. Larson, Frames for Banach spaces,Contemp. Math. 247 (1999), 149–182.

P.G. CasazzaandO. Christensen,Perturbationof operatorand applicationsto frame theory, J.Fourier Anal. Appl. 3(1997), 543–557.

O. Christensen andC. Heil,Perturbationof Banach frames and atomic decomposition, Math. Nachr. 185 (1997), 33–47.

O. Christensen,Frames and Bases (An Introductory Course), Birkhauser, Boston (2008).

R.R. Coifman and G.Weiss, Extension of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), 569–645.

I. Daubechies, A. Grossmann and Y. Meyer, Painless non-orthogonal expansions, J. Math. Phys. 27 (1986), 1271–1283.

R.J. Duffin and A.C. Schaeffer, A class of non-harmonic Fourier series, Trans. Amer. Math. Soc. 72 (1952), 341–366.

N. Dunford and J.T. Schwartz, Linear Operator, Vol. I, Interscience Publishers, New York, London, 1958.

H.G. Feichtinger and K. Grochenig, A unified approach to atomic decopostion via integrable group representations, Lecture Notes in Mathematics 1302, Springer, Berlin, 1988, 52–73.

S.J. Favier and R.A. Zalik, On the stability of frames ans Reisz bases, Appl. Comp. Harm. Anal. 2 (1995), 160–173.

D. Gabor, Theory of communications, Jour.Inst. Elec. Engg. 93(1946), 429–457.

K. Grochenig, Describing function: atomic decompositions versus frames, Montash. Math. 112(1991), 1–41.

D. Han and D.R. Larson, Frames, bases and group representations, Mem. Amer. Math. Soc. 147(697) (2000), 1–91.

P.K. Jain, S.K. Kaushik and L.K.Vashisht,On Banach frames,Indian J. Pure Appl. Math. 37(5) (2006), 265–272.

S.K. Kaushik,A note on exact Banach frames, Int. J. Pure Appl. Math. 31(2) (2006), 279–286.

S.K. Kaushik, Some results concerning frames in Banach spaces, Tamking J. Math. 37(5) (2007), 267–276.

I. Singer, Bases in Banach Spaces II, Springer, NewYork, 1981.

L.K. Vashisht, On retro Banach frames of type P, Azerbaijan J. Math. 2(1) (2012), 82–89.

L.K.Vashisht,On framesin Banach spaces, Commun. Math. Appl., preprint.

K. Yoshida, Functional Analysis, Springer-Verlag, Berlin ” Heidelber ” New York, 1966.

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CITATION

How to Cite

Vashisht, L. K., & Sharma, S. (2012). On Weighted Banach Frames. Communications in Mathematics and Applications, 3(3), 283–292. https://doi.org/10.26713/cma.v3i3.212

Issue

Vol. 3 No. 3 (2012)

Section

Research Article

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