References

  1. Ahmad O., Shah F.A., Sheikh N.A. Gabor frames on non-Archimedean fields. Int. J. Geom. Methods Mod. Phys. 2018, 15, 1850079 (17 pages). doi: 10.1142/S0219887818500792
  2. Christensen O. An Introduction to Frames and Riesz Bases. Birkhäuser, Boston, 2016.
  3. Daubechies I., Grossmann A., Meyer Y. Painless non-orthogonal expansions. J. Math. Phys. 1986, 27 (5), 1271-1283. doi: 10.1063/1.527388
  4. Duffin R.J., Shaeffer A.C. A class of nonharmonic Fourier series. Trans. Amer. Math. Soc. 1952, 72, 341-366. doi: 10.2307/1990760
  5. Farkov Yu.A. Orthogonal $p$-wavelets on $\mathbb R^+$. In: Proc. Int. Conf. Wavelets and Splines, St. Peterburg State University, 4-26, 2005.
  6. Farkov Yu.A., Rodionov E.A. Nonstationary wavelets related to the Walsh functions. Amer. J. Comput. Math. 2012, 2, 82-87. doi: 10.4236/ajcm.2012.22011
  7. Farkov Yu.A. On wavelets related to Walsh series. J. Approx. Theory 2009, 161, 259-279. doi: 10.1016/j.jat.2008.10.003
  8. Gabor D. Theory of communications. J. Inst. Elect. Engn. 1946, 93, 429-457.
  9. Gröchenig K., Janssen A.J., Kaiblinger N., Pfander G. Note on $B$-splines, wavelet scaling functions, and Gabor frames. IEEE Trans. Inform. Theory 2003, 49 (12), 3318-3320. doi: 10.1109/TIT.2003.820022
  10. Gröchenig K. Foundation of Time-Frequency Analysis. Birkhäuser, Boston, 2001.
  11. Golubov B.I., Efimov A.V., Skvortsov V.A. Walsh Series and Transforms: Theory and Applications. Kluwer, Dordrecht, 1991.
  12. Ron A., Shen Z. Weyl-Heisenberg frames and Riesz bases in $L^2(\mathbb R^d )$. Duke Math. J. 1997 89 (2), 237-282. doi: 10.1215/S0012-7094-97-08913-4
  13. Schipp F., Wade W.R., Simon P. Walsh Series: An Introduction to Dyadic Harmonic Analysis. Adam Hilger, Bristol and New York, 1990.
  14. Shah F.A. Gabor frames on a half-line. J. Contemp. Math. Anal. 2012, 47 (5), 251-260. doi: 10.3103/S1068362312050056
  15. Shah F.A., Ahmad O., Sheikh N.A. Orthogonal Gabor systems on local fields. Filomat 2017, 31 (16), 5193-5201. doi: 10.2298/FIL1716193S
  16. Shah F.A., Ahmad O. Wave packet systems on local fields. J. Geom. Phys. 2017, 120, 5-18. doi: 10.1016/j.geomphys.2017.05.015
  17. Shah F.A., Ahmad O., Rahimi A. Frames Associated with Shift Invariant Spaces on Local Fields. Filomat 2018, 32 (9), 3097-3110. doi: 10.2298/FIL1809097S
  18. Zhang Y. Walsh Shift-Invariant Sequences and p-adic Nonhomogeneous Dual Wavelet Frames in $L^2(\mathbb R^+)$. Results Math. 2019, 74, 111, 26 pp. doi: 10.1007/s00025-019-1034-7