Geodesic
Approximations of the exponential function and relative closeness of stable signals
Sbornik. Mathematics, Tome 74 (1993) no. 2, pp. 291-307 
L. A. Balashov; Yu. A. Dreizin; M. S. Mel'nikov. Approximations of the exponential function and relative closeness of stable signals. Sbornik. Mathematics, Tome 74 (1993) no. 2, pp. 291-307. http://geodesic.mathdoc.fr/item/SM_1993_74_2_a1/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The results presented here are based on the use of approximations of analytic functions in certain questions involving numerical methods for “physical” equations. The concepts of relative closeness and of stability of signals are introduced. A simple method is given for approximate inversion of the Laplace transformation, with an estimate of the relative error. Also, estimates are obtained for the dimensions of spaces in which it is possible to find approximate solutions of multidimensional systems of linear equations, as a function of the accuracy of approximation and the “size” of the spectrum of the operator.

[1] Vyurkov V. V., Dreizin Yu. A., “O vychislenii polei dipolei v provodyaschikh sloistykh sredakh”, DAN SSSR, 262:5 (1982), 1108–1112

[2] Dreizin Yu. A., “Ob ispolzovanii analiticheskikh svoistv elektromagnitnykh otklikov dlya obrabotki signalov zondirovanii”, II Vsesoyuznaya shkola-seminar po elektromagnitnym zondirovaniyam, Tezisy dokladov, Izd-vo MGU, M., 1981

[3] Svetov B. S., Barsukov P. O., “Ob ispolzovanii predstavleniya effektov stanovleniya polya v vide superpozitsii eksponentsialno zatukhayuschikh elementarnykh protsessov”, Izmerenie i obrabotka odinochnykh signalov pri geofizicheskikh issledovaniyakh, Izd-vo KFAN SSSR, Apatity, 1979

[4] Buslaev V. I., Vitushkin A. G., “Otsenka dliny koda signalov s konechnym spektrom v svyazi s zadachami zvukozapisi”, Izv. AN SSSR. Ser. matem., 38:4 (1984), 867–895 | MR

[5] Kirillov A. A., Gvishiani A. D., Teoremy i zadachi funktsionalnogo analiza, Nauka, M., 1979 | MR

[6] Nikolskii N. K., Lektsii ob operatore sdviga, Nauka, M., 1980 | MR

[7] Gradshtein I. S., Ryzhik I. M., Tablitsy integralov, summ, ryadov i proizvedenii, Fizmatgiz, M., 1963 | MR