@article{SM_1999_190_8_a3,
author = {E. E. Petrov},
title = {Paley{\textendash}Wiener theorems for the~matrix {Radon} transform},
journal = {Sbornik. Mathematics},
pages = {1173--1193},
year = {1999},
volume = {190},
number = {8},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1999_190_8_a3/}
}
E. E. Petrov. Paley–Wiener theorems for the matrix Radon transform. Sbornik. Mathematics, Tome 190 (1999) no. 8, pp. 1173-1193. http://geodesic.mathdoc.fr/item/SM_1999_190_8_a3/
[1] Gelfand I. M., Graev M. I., Vilenkin N. Ya., Integralnaya geometriya i svyazannye s nei voprosy teorii predstavlenii, Fizmatgiz, M., 1962
[2] Khelgason S., Gruppy i geometricheskii analiz, Mir, M., 1987 | MR
[3] Petrov E. E., “Preobrazovanie Radona v prostranstve matrits”, Tr. sem. po vekt. i tenz. analizu, 1970, no. 15, 299–315 | MR
[4] Gelfand I. M., Graev M. I., “Integraly po giperploskostyam osnovnykh i obobschennykh funktsii”, Dokl. AN SSSR, 135:6 (1960), 1307–1310 | MR | Zbl
[5] Gelfand I. M., Gindikin S. G., Graev M. I., “Integralnaya geometriya v affinnom i proektivnom prostranstvakh”, Itogi nauki i tekhniki. Sovr. problemy matem., 16, VINITI, M., 1980, 53–226 | MR
[6] Semyanistyi V. I., “O nekotorykh integralnykh preobrazovaniyakh v evklidovom prostranstve”, Dokl. AN SSSR, 134:3 (1960), 536–539 | MR | Zbl
[7] Ludvig D., “The Radon transform in Euclidean space”, Comm. Pure Appl. Math., 19 (1966), 49–81 | MR
[8] Laks P. D., Fillips R. S., “Teorema Peli–Vinera dlya preobrazovaniya Radona”, Matematika. Sb. per., 16:3 (1972), 97–112
[9] Smith K. T., Solmon D. C., Wagner S. L., “Practical and mathematical aspects of the problem of reconstructing objects from radiographs”, Bull. Amer. Math. Soc., 83 (1977), 1227–1270 | DOI | MR | Zbl
[10] Solmon D. C., “Asymptotic formulas for the dual Radon transform and applications”, Math. Z., 195 (1987), 321–343 | DOI | MR | Zbl
[11] Petrov E. E., “Teorema Peli–Vinera dlya kompleksa Radona”, Izv. vuzov. Matem., 1977, no. 3, 66–77 | Zbl
[12] Graev M. I., “Integralnaya geometriya na prostranstve $L^n$, gde $L$ – koltso matrits”, Funkts. analiz i ego pril., 30:4 (1996), 71–74 | MR | Zbl
[13] Gonzalez F. B., “Invariant differential operators and the range of the Radon $d$-plane transform”, Math. Ann., 287:4 (1990), 627–635 | DOI | MR | Zbl
[14] Petrov E. E., “Uslovie Kavaleri dlya integralov po $k$-mernym ploskostyam, $k$”, Algebra i analiz, 5:4 (1993), 191–205
[15] Chernov V. G., “Odnorodnye obobschennye funktsii i preobrazovanie Radona v prostranstve pryamougolnykh matrits nad nepreryvnym lokalno kompaktnym nesvyaznym polem”, Dokl. AN SSSR, 191:3 (1970), 540–543 | MR | Zbl
[16] Khua Lo-Ken, Garmonicheskii analiz funktsii mnogikh kompleksnykh peremennykh v klassicheskikh oblastyakh, IL, M., 1959
[17] Quinto E. T., “The invertibility of rotation invariant Radon transforms”, J. Math. Anal. Appl., 91 (1983), 510–522 | DOI | MR | Zbl