Geodesic
Solution to integral equations with $\delta$-like kernel
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 7 (2004) no. 3, pp. 229-240.

Voir la notice de l'article provenant de la source Math-Net.Ru

The subject of consideration is the integral equations with $\delta$-like kernel which result from the processing of physical process spectra, in the impulse technique, as well as in the time series analysis. Solution and estimates of the integral equations by the Gaussian or the Legendre least squares methods and by their regularized forms, like the orthogonal projections method, are well known. Here, contrary to the mentioned methods, the analysis focuses on the form of the least-squares method which uses the integral function theory, when the spectrum and length of the function are in the uncertainty principle relation. 
@article{SJVM_2004_7_3_a4,
     author = {E. l. Zhukovskii},
     title = {Solution to integral equations with $\delta$-like kernel},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {229--240},
     publisher = {mathdoc},
     volume = {7},
     number = {3},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2004_7_3_a4/}
}
TY  - JOUR
AU  - E. l. Zhukovskii
TI  - Solution to integral equations with $\delta$-like kernel
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2004
SP  - 229
EP  - 240
VL  - 7
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJVM_2004_7_3_a4/
LA  - ru
ID  - SJVM_2004_7_3_a4
ER  - 
%0 Journal Article
%A E. l. Zhukovskii
%T Solution to integral equations with $\delta$-like kernel
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2004
%P 229-240
%V 7
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJVM_2004_7_3_a4/
%G ru
%F SJVM_2004_7_3_a4
E. l. Zhukovskii. Solution to integral equations with $\delta$-like kernel. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 7 (2004) no. 3, pp. 229-240. http://geodesic.mathdoc.fr/item/SJVM_2004_7_3_a4/

[1] Lavrentev M. M., O nekotorykh nekorrektnykh zadachakh matematicheskoi fiziki, Novosibirsk, 1962 | MR

[2] Khalfin L. A., Informatsionno-statisticheskaya teoriya opticheskikh i spektralnykh priborov, Kurs lektsii na fiz. fak. LGU, 1960–1961 | Zbl

[3] Vakman D. E., Slozhnye signaly i printsip neopredelennosti v radiolokatsii, Sov. radio, M., 1965

[4] Zhukovskii E. L., Pliskin S. Yu., “Printsip neopredelennosti i regulyarizatsiya lineinykh sistem algebraicheskikh uravnenii”, DAN SSSR, 262:6 (1982), 1301–1304 | MR

[5] Phillips D. Z., “A technique for the numerical solution of certain integral equations of the first kind”, J. Assoc. Comput. Mach., 9:1 (1962), 84–97 | MR | Zbl

[6] Tikhonov A. H., Shevchenko V. G., Zaikin P. N., Ishkhanov B. S., Mechenov A. S., “O raschete secheniya fotoyadernoi reaktsii po eksperimentalnoi informatsii”, Vestnik MGU, ser. fizika, 1973, no. 3, 317

[7] Albert A., Regressiya, psevdoinversiya i rekurrentnoe otsenivanie, Nauka, M., 1977 | MR

[8] Zhukovskii E. L., Meleshko V. I., “Metod ortogonalnoi proektsii i ego regulyarizovannaya i statisticheskaya interpretatsiya”, Zhurn. vychisl. matem. i mat. fiziki, 38:5 (1998), 724–727 | MR | Zbl

[9] Khurgin Ya. I., Yakovlev V. P., Finitnye funktsii v fizike i tekhnike, Nauka, M., 1971 | Zbl

[10] Fedotov A. M., Nekorrektnye zadachi so sluchainymi oshibkami v dannykh, Nauka. Sib. otd-nie, Novosibirsk, 1990 | MR

[11] Tsypkin Ya. Z., Osnovy informatsionnoi teorii identifikatsii, Nauka, M., 1984 | MR

[12] Smirnov N. V., Dunin-Barkovskii I. V., Kurs teorii veroyatnostei i matematicheskoi statistiki dlya tekhnicheskikh prilozhenii, Nauka, M., 1965 | MR

[13] Marpl-ml. S. L., Tsifrovoi spektralnyi analiz i ego prilozheniya, Mir, M., 1990

[14] Burg T. P., Maximum entropy spectral analysis, 37-th Meeting Soc. Explor. Geophys., Oklahoma City, 1967

[15] Turchin V. F., Kozlov V. P., Malkevich M. S., “Ispolzovanie matematicheskoi statistiki dlya resheniya nekorrektnykh zadach”, Uspekhi fizicheskikh nauk, 102:3 (1970), 345–386

[16] Zhukovskii E. L., “Optimizatsionnye zadachi v obrabotke i interpretatsii dannykh”, Izvestiya Akademii nauk. Teoriya i sistemy upravleniya, 2002, no. 1, 20–35 | MR