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Keywords:
singular convolution equations; fast Fourier transform; tempered distribution; polynomial transfer functions; simple zeros
singular convolution equations; fast Fourier transform; tempered distribution; polynomial transfer functions; simple zeros
Summary:
The inverse Fast Fourier Transform is a common procedure to solve a convolution equation provided the transfer function has no zeros on the unit circle. In our paper we generalize this method to the case of a singular convolution equation and prove that if the transfer function is a trigonometric polynomial with simple zeros on the unit circle, then this method can be extended.
References:
[1] Babuška, I.: The Fourier transform in the theory of difference equations and its applications. Arch. Mech. 11 (1959), 349-381. MR 0115030 | Zbl 0092.12201
[2] Beals, R.: Advanced Mathematical Analysis. GTM 12. Springer New York-Heidelberg-Berlin (1973). MR 0530403
[3] Fisher, B.: The product of distributions. Q. J. Math. 22 (1971), 291-298. DOI 10.1093/qmath/22.2.291 | MR 0287308 | Zbl 0213.13104
[4] Jarchow, H.: Locally Convex Spaces. B. G. Teubner Stuttgart (1981). MR 0632257 | Zbl 0466.46001
[5] Rudin, W.: Functional Analysis. McGraw-Hill New York (1973). MR 0365062 | Zbl 0253.46001
[6] Vitásek, E.: Periodic distributions and discrete Fourier transforms. Pokroky mat., fyz. astronom. 54 (2009), 137-144 Czech.
[7] Walter, G. G.: Wavelets and Other Orthogonal Systems with Applications. CRC Press Boca Raton (1994). MR 1300204 | Zbl 0866.42022
[8] Walsh, J. L., Sewell, W. E.: Note on degree of approximation to an integral by Riemann sums. Am. Math. Monthly 44 (1937), 155-160. DOI 10.2307/2301660 | MR 1523881 | Zbl 0016.29901
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