GENERALIZED ATOMIC WAVELETS
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Novikov, I. Ya., Stechkin, S. B. Basic wavelet theory. Russian Math. Surveys, 1990, vol. 53, no. 6, pp. 1159-1231.
Welstead, S. Fractal and wavelet image compression techniques. SPIE Press, 1999. 256 p.
Meyer, F. G., Petrossian, A. A. Wavelets in signal and image analysis. Springer, 2001. 556 p.
Stollnitz, E. J., DeRose, T. D., Salesin, D. H. Wavelets for computer graphics: theory and applications. Morgan Kaufmann Publ., 1996. 246 p.
Cohen, J., Zayed, A. I. (eds.). Wavelets and multiscale analysis: theory and applications. Springer, 2011. 353 p.
Hramov, A. E., Koronovsky, A. A., Makarov, V. A., Pavlov, A. N., Sitnikova, E. Wavelets in Neuroscience. Springer, 2015. 331 p.
Chandrasekhar, E., Dimri, V. P., Gadre, V. M. Wavelets and fractals in Earth system sciences. CRC Press, 2014. 294 p.
Farouk, M. H. Application of wavelets in speech processing. Springer, 2014. 53 p.
Chan, A. K., Goswavi, J. C. Fundamentals of wavelets: theory, algorithms and applications. John Wiley and sons, 2011. 359 p.
Gencay, R., Selcuk, F., Whitcher, B. An introduction to wavelets and other filtering methods in finance and economics. Academic press, 2002. 359 p.
Gallegati, M., Semmler, W. (eds.). Wavelet applications in economics and finance. Springer, 2014. 261 p.
Rvachev, V. L., Rvachev, V. A. Neklassicheskie metody teorii priblizhenii v kraevykh zadachakh [Nonclassical methods of approximation theory in boundary value problems]. Kyiv, “Naukova dumka” Publ., 1979. 196 p.
Rvachev, V. A. Compactly supported solutions of functional-differential equations and their applications. Russian Math. Surveys, 1990, vol. 45, no. 1, pp. 87 – 120.
Spiridonov, V. Vsplesk revolyutsii [Splash of revolutions]. Available at: http://old.computerra.ru /1998/236/193919/ (accessed 12.01.2018).
Rvachev, V.A. On approximation by means of the function up(x). Sov. Math. Dokl. 1977, vol. 233, no. 2, pp. 295-296.
Gotovac, H., Cvetkovic, V., Andricevic, R. Adaptive Fup multi-resolution approach to flow and advective transport in highly heterogeneous porous media: methodology, accuracy and convergence. Adv. Water Resour., 2009, vol. 32, no. 6, pp. 885-905.
Gotovac, H., Andricevic, R., Gotovac, B. Multi-resolution adaptive modeling of groundwater flow and transport problems. Adv. Water Resour., 2007, vol. 30, vo. 5, pp. 1105-1126.
Lazorenko, O. V. The use of atomic functions in the Choi-Williams analysis of ultrawideband signals. Radioelectronics and Communications Systems, 2009, vol. 52, pp. 397-404.
Ulises Moya-Sanchez, E., Bayro - Corrocha-no, E. Quaternionic analytic signal using atomic functions. Porgress in Pattern Recognition, Image Analysis, Computer Vision, and Applications, Lecture Note in Computer Science., 2012, vol. 7441, pp. 699-706.
Dyn, N., Ron, A. Multiresolution analysis by infinitely differentiable compactly supported functions. Appl. Comput. Harmon. Anal., 1995, vol. 2, no. 1, pp. 15-20.
Cooklev, T., Berbecel, G. I., Venetsanopou-los, A. N. Wavelets and differential-dilatation equations. IEEE Transactions on signal processing, 2000, vol. 48, no. 8, pp. 670-681.
Charina, M., Stockler, J. Tight wavelet frames for irregular multiresolution analysis. Appl. Comput. Harmon. Anal., 2008, vol. 25, no. 1, pp. 98-113.
Makarichev, V. A. Approximation of periodic functions by mups(x). Math. Notes, 2013, vol. 93, no. 6, pp. 858-880.
Makarichev, V. A. Ob odnoi nestatsionarnoi sisteme beskonechno differentsiruemykh veievletov s kompaktnym nositelem [On the nonstationary system of infinitely differentiable wavelets with a compact support]. Visnyk KhNU, Ser. “Matematika, prikladna matematika and meckhanika”, 2011, no. 967, pp. 63-80.
Brysina, I. V., Makarichev, V. A. Atomic wavelets. Radioelektronni i komp'uterni sistemi - Radioelectronic and computer systems, 2012, vol. 53, no. 1, pp. 37-45.
Makarichev, V. A. The function mups(x) and its applications to the theory of generalized Taylor series, approximation theory and wavelet theory. Contemporary problems of mathematics, mechanics and computing sciences, Kharkiv, “Apostrophe” Publ., 2011, pp. 279-287.
Makarichev, V. O. Application of atomic functions to lossy image compression. Theoretical and applied aspects of cybernetics. Proceedings of the 5th International scientific conference of students and young scientists. Kyiv, “Bukrek” Publ., 2015, pp. 166-175.
Brysina, I. V., Makarichev, V. A. Approximation properties of generalized Fup-functions. Visnyk of V. N. Karazin Kharkiv National University, Ser. “Mathematics, Applied Mathematics and Mechanics”, 2016, vol. 84, pp. 61-92.
Brysina, I. V., Makarichev, V. A. On the asymptotics of the generalized Fup-functions. Adv. Pure Appl. Math., 2014, vol. 5, no. 3, pp. 131-138.
DOI: https://doi.org/10.32620/reks.2018.1.03
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