Geodesic
Asymptotics of Fourier coefficients and the convergence of expansions over an oscillatory basis
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 43 (2003) no. 1, pp. 81-94 
S. Yu. Igashov. Asymptotics of Fourier coefficients and the convergence of expansions over an oscillatory basis. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 43 (2003) no. 1, pp. 81-94. http://geodesic.mathdoc.fr/item/ZVMMF_2003_43_1_a6/
@article{ZVMMF_2003_43_1_a6,
     author = {S. Yu. Igashov},
     title = {Asymptotics of {Fourier} coefficients and the convergence of expansions over an oscillatory basis},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {81--94},
     year = {2003},
     volume = {43},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2003_43_1_a6/}
}
TY  - JOUR
AU  - S. Yu. Igashov
TI  - Asymptotics of Fourier coefficients and the convergence of expansions over an oscillatory basis
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2003
SP  - 81
EP  - 94
VL  - 43
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2003_43_1_a6/
LA  - ru
ID  - ZVMMF_2003_43_1_a6
ER  - 
%0 Journal Article
%A S. Yu. Igashov
%T Asymptotics of Fourier coefficients and the convergence of expansions over an oscillatory basis
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2003
%P 81-94
%V 43
%N 1
%U http://geodesic.mathdoc.fr/item/ZVMMF_2003_43_1_a6/
%G ru
%F ZVMMF_2003_43_1_a6

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

[1] Yamani H. A., Fishman L., “$J$-matrix method: Extensions to arbitrary angular momentum and to Coulomb scattering”, J. Math. Phys., 16:2 (1975), 410–420 | DOI | MR | Zbl

[2] Filippov G. F., Okhrimenko I. P., “O vozmozhnosti ispolzovaniya ostsillyatornogo bazisa dlya resheniya zadach nepreryvnogo spektra”, Yadernaya fiz., 32:4 (1980), 932–939

[3] Filippov G. F., “Ob uchete pravilnoi asimptotiki v razlozheniyakh po ostsillyatornomu bazisu”, Yadernaya fiz., 33:4 (1981), 928–931

[4] Okhrimenko I. P., “Allowance for the Coulomb interaction in the framework of an algebraic version of the resonating group method”, Nucl. Phys. A, 424 (1984), 121–142 | DOI

[5] Mikhlin S. G., Variatsionnye metody v matematicheskoi fizike, Nauka, M., 1970 | MR | Zbl

[6] Igashov S. Yu., “Ob asimptotike matrichnykh elementov kulonovskogo vzaimodeistviya v ostsillyatornom predstavlenii v okrestnosti glavnoi diagonali”, Yadernaya fiz., 60:12 (1997), 2202–2204

[7] Shirokov A. M., Smirnov Yu. F., Zaitsev S. A., “Istinno mnogochastichnoe rasseyanie v ostsillyatornom predstavlenii”, Teor. i matem. fiz., 117:2 (1998), 227–248 | MR | Zbl

[8] Vasilevsky V. S., Arickx F., “Algebraic model for quantum scattering: Reformulation, analysis, and numerical strategies”, Phys. Rev. A, 55:1 (1997), 265–286 | DOI

[9] Bang J. M., Mazur A. I., Shirokov A. M. et al., “$P$-matrix and $J$-matrix approaches: Coulomb asymptotics in the harmonic oscillator representation of scattering theory”, Ann. Phys., 280 (2000), 299–335 | DOI | Zbl

[10] Filippov G. F., Rybkin I. Yu., Korennov S. V., Kato K., “On the complete basis of Pauli-allowed states of three-cluster systems in the Fock–Bargmann space”, J. Math. Phys., 36:9 (1995), 4571–4589 | DOI | MR | Zbl

[11] Filippov G. F., Kato K., Korennov S. V., “He as a three-cluster system — investigation of the ground state and the continuum $0^+$ states”, Progr. Theor. Phys., 96:3 (1996), 575–595 | DOI

[12] Kruppa A. T., Arai K., “Resonances and the continuum level density”, Phys. Rev. A, 59:5 (1999), 3556–3561 | DOI

[13] Arai K., Kruppa A. T., “Continuum level density in a microscopic cluster model: Parameters of resonances”, Phys. Rev. C, 60:6 (1999), 064315 | DOI | MR

[14] Smirnov Yu. F., Stotland L. Ya., Shirokov A. M., “Polyusa $S$-matritsy v diskretnom predstavlenii”, Izv. AN SSSR. Ser. fiz., 54:5 (1990), 897–906

[15] Rubtsova O. A., Kukulin V. I., “Novyi podkhod k resheniyu zadachi rasseyaniya sostavnoi chastitsy v pole yadra”, Yadernaya fiz., 64:9 (2001), 1769–1783

[16] Levitan B. M., Sargsyan I. S., Vvedenie v spektralnuyu teoriyu, Nauka, M., 1970 | MR

[17] Levitan B. M., Sargsyan I. S., Operatory Shturma–Liuvillya i Diraka, Nauka, M., 1988 | MR | Zbl

[18] Askey R., Wainger S., “Mean convergence of expansions in Laguerre and Hermite series”, J. Math. Phys., 87:3–4 (1965), 695–708 | MR | Zbl

[19] Muckenhoupt B., “Mean convergence of Hermite and Laguerre series. I; II”, Trans. Amer. Math. Soc., 147 (1970), 419–431 ; 433–460 | DOI | MR | Zbl

[20] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii, Nauka, M., 1974

[21] Spravochnik po spetsialnym funktsiyam, eds. Abramovits M., Stigan I., Nauka, M., 1983

[22] Sege G., Ortogonalnye mnogochleny, Fizmatgiz, M., 1962

[23] Suetin P. K., Klassicheskie ortogonalnye mnogochleny, 2-e izd., Nauka, M., 1979 | MR | Zbl

[24] Olver F., Asimptotika i spetsialnye funktsii, Nauka, M., 1990 | MR | Zbl

[25] Igashov S. Yu., “Asymptotic approximation and weight estimate for the Laguerre polynomials”, Integral Transforms and Spec. Functions, 8:3–4 (1999), 209–216 | DOI | MR | Zbl

[26] Igashov S. Yu., Ob asimptotike koeffitsientov Fure v razlozheniyakh po sisteme ostsillyatornykh funktsii, Preprint MIFI-016-98, MIFI, M., 1999 | MR

[27] Erdelyi A., “Asymptotic forms for Laguerre polynomials”, J. Indian Math. Soc., 24 (1960), 235–250 | MR

[28] Prudnikov A. P., Brychkov Yu. A., Marichev O. I., Integraly i ryady. Spetsialnye funktsii, Nauka, M., 1983 | MR | Zbl

[29] Prudnikov A. P., Brychkov Yu. A., Marichev O. I., Integraly i ryady. Elementarnye funktsii, Nauka, M., 1981 | MR | Zbl