SOME RESULTS ON GEOMETRIC PROPERTIES OF FRAMES IN BANACH SPACES
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Keywords:
Frames, Banach frames, Exact frame, Frame; Atomic System, Cone, A-modulusAbstract
In this paper, we have defined A- cone and related concepts in Banach spaces and prove a result concerning convergence of a sequence in an A- cone. Also, atomic system for a subset of a Banach space is defined and proved that if a Banach space has an atomic system, then every subset of it also has an atomic system.
References
P. G. Casazza, D. Han and D. R. Larson, Frames for Banach spaces, Contemp. Math.,
(1999), 149-182.
R.J.Duffin and A.C.Schaeffer, A class of nonharmonic Fourier serier. Trans. Am. Math.
Soc. 72(1952), 341–366.
O. Christensen , An introduction to Frames and Riesz Bases, Birkhauser, (2nd Edn.)
R.R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull.
Amer. Math. Soc., 83 (1977) 569-645.
Daubechies,I., Grossman,A. and Meyer,Y. Painless non-orthogonal expansions, J. Math.
Physics, 27, 1271-1283, (1986).
H. Ellouz, Some Properties of K-Frames in Quaternionic Hilbert Spaces, Complex Anal.
Oper. Theory 14, 8 (2020). doi.org/10.1007/s11785- 019-00964-5.
H.G.Feichtinger and K.H.Grochenig,Banach spaces related to integrable group representation
and their atomic decomposition, I J.Funct.Anal.,86(1989),307-340.
H. Feichtinger and A. Janssen. Validity of WH-frame bound conditions depends on lattice
parameters. Applied and Computational Harmonic Analysis, 8(1):104–112, 2000.
H. Feichtinger and N. Kaiblinger. Varying the time-frequency lattice of Gabor frames.
Transactions of the American Mathematical Society, 356(5):2001–2023, 2004.
H. G. Feichtinger, K. Gr¨ochenig, and D.Walnut. Wilson bases and modulation spaces.
Mathematische Nachrichten, 155(1):7–17, 1992.
J. P. Gabardo and D. Han. Subspace Weyl-Heisenberg frames. Journal of Fourier Analysis
and Applications, 7(4):419–433, 2001.
K.Grochenig, Describing functions: atomic decompositions versus frames. Monatsh.
Math. 112(1991), 1–41.
S Jahan, V Kumar, and C. Shekhar, Cone associated with frames in Banach Spaces
Palestine Journal of Mathematics Vol. 7, no. 2 (2018), 641–649.
P.K.Jain, S.K.Kaushik and L.K. Vashisht , Banach frames for conjugate Banach
spaces,Zeitschrift fur Anal. und ihre Anwend ungen , 23(4)(2004) , 713-720.
Jha, N.N. and Sharma,S., Block Sequences and Retro Banach Frames, Poincare Journal
of Analysis and Applications, 7 (2), 267-274, (2020).
S. Katre, A. Goswami, P. Mishra, J. Bapat, and D. Das. Impact of variable MTU size
of voice packet to reduce packet loss in bandwidth constraint military network. In 2019
IEEE 5th International Conference for Convergence in Technology (I2CT), pages 1–5.
IEEE, 2019.
F. L. Lewis. Wireless sensor networks. Smart Environments: Technologies, Protocols, and
Applications, pages 11–46, 2004.
B. Muraleetharan and K. Thirulogasanthar, Fredholm operators and essential S-spectrum
in the quaternionic setting, Journal of Mathematical Physics 59.10 (2018), 103506.
P.A. Terekhin, Frames in Banach spaces. Funct. Anal its Appl 44, 199–208 (2010).
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