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By Victor F. Kravchenko

During this monograph, the unconventional promising traits in adaptive electronic processing of multidimensional 1D–3D signs with varied purposes to radio physics, radio engineering, and medication are thought of

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Theorem 4. 58) where [a] is the integral part of a number a. At s = 1 these formulas are reduced to xm,n,1 1 up m (xm,n,1 ) = m! (n+1) up m . 11. Atomic Functions πm(x) Consider the functional-differential equation 2m−1 ′ πm (x) = a πm (x1 (m)) + k=2 (−1)k πm (xk (m)) − πm (x2m (m)) , where xk (m) = 2mx + 2m − 2k + 1, x ∈ R1 , k = 1, 2m, m = 3, 4, 5, . . 60) 30 Ch. 1. 60) and denote by Fm (t). Then, the latter equality will take the form ∞ ixt πm (x)dx −∞ e 2m−1 a −itFm (t) = e−it 2m + 2m 2m−1 (−1)k eit 2k−1−2m 2m k=2 − eit 2m−1 2m Fm (t/2m) .

F. and Zamyatin, A. A. Approximation Properties of Atomic Functions under Solving Electrodynamics Integral Equations by the Method of Moments. Dokl. Akad. Nauk, 1999, vol. 365, no. 4, pp. 475–477. 19. Basarab, M. A. and Kravchenko, V. F. The Construction of Equations for Boundaries of Fractal Domains with the Use of the R-function Method. Telecommunications and Radio Engineering, 2001, vol. 56, no. 12, pp. 2–13. 20. Zelkin, E. , Kravchenko, V. , Pustovoit, V. , and Timoshenko, V. V. Approximation of Any Function by the Integer Functions of the Exponential Type.

118–137. 9. Kravchenko, V. F. and Rvachev, V. A. Wavelet-Systems and Their Application in Signal Processing. Zarubezhnaya Radioelektronika. Uspekhi Sovremennoi Radioelektroniki, 1996, no. 4, pp. 3–20. 10. Kravchenko, V. F. and Basarab, M. A. New Methods of Signal Filtering Based on Atomic Functions, Proc. of The Fourth International Symposium «Physics and Engineering of Millimeter and Sub-Millimeter Waves», June 4–9, 2001, Kharkov, Ukraine, vol. 1, pp. 235–237. 11. Kravchenko, V. F. and Basarab, M.

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