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Localization algorithms for singularities of solutions to convolution equations of the first kind. (English) Zbl 1158.65087
The authors construct and investigate localization algorithms for isolated singularities of a solution of a linear convolution equation of the first kind whose right-hand side to be given using an averaging method defined by an averaging functional to obtain the singularities and using the Fourier transform.

##### MSC:
 65R20 Numerical methods for integral equations 45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
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##### References:
 [1] Yu V., Uspehi Fiz. Nauk 165 pp 2– (1995) [2] Kozlov V. P., Optics and Spectroscopy 16 pp 3– (1964) [3] Kozlov V. P., Optics and Spectroscopy 17 pp 2– (1964) [4] Ageev A. L., Computing Methods and Programming 8 pp 275– (2007) [5] Kostousov V. B., Proc. of Mathematics and Mechanics Institute. Ekaterinburg pp 11– (2005) [6] Ageev A. L., Izv. Vuzov. Matematika 11 pp 1– (2007) [7] Antonova T. V., Izv. Vuzov. Matematika 7 pp 65– (2001) [8] Antonova T. V., J. Inv. Ill-Posed Problems 10 pp 2– (2002) [9] Antonova T. V., Fiziki 40 pp 6– (2000) [10] Antonova T. V., VINITI 17.10 00 pp 2639– (2000) [11] Antonova T. V., Proc. of the Steklov Institute of Mathematics 1 pp 145– (2002) [12] Ageev A. L., Computation Mathematics and Mathematical Physics 48 pp 8– (2008)
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