Geodesic
Partial Jost determinants and spectral density of the resolvent with respect to the momentum transfer
Teoretičeskaâ i matematičeskaâ fizika, Tome 81 (1989) no. 1, pp. 45-58 Cet article a éte moissonné depuis la source Math-Net.Ru

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Integral representations for partial lost determinants and lost operator on the unit sphere are derived in terms of the spectral density in the momentum transfer of the elliptic operator resolvent in $R_N$. The connection is found between the spectral densities for the potential $V(r)$ in different dimensions $r_N$, $N\geqslant2$. New integral representations for the solutions of the Coulomb problem are obtained. 
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     title = {Partial {Jost} determinants and spectral density of the resolvent with respect to~the momentum transfer},
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S. È. Korenblit. Partial Jost determinants and spectral density of the resolvent with respect to the momentum transfer. Teoretičeskaâ i matematičeskaâ fizika, Tome 81 (1989) no. 1, pp. 45-58. http://geodesic.mathdoc.fr/item/TMF_1989_81_1_a4/

[1] Fubini S., Stroffolini R., Theoretical Physics, Lecture (Trieste, 1962), Int. Atom Ener. Agency, Vienna, 1963, 365; 379

[2] De Alfaro V., Redzhe T., Potentsialnoe rasseyanie, Mir, M., 1966 | Zbl

[3] t'Hooft G., Phys. Rev., D14 (1976), 3432–3450 ; Callan C., Coleman S., Phys. Rev., D16 (1977), 176–178

[4] Nyuton R., Teoriya rasseyaniya voln i chastits, Mir, M., 1969 ; Brown, Fivel, Lee, Sawyer, Ann. Phys., 23 (1963), 187 | MR | DOI | MR

[5] Korenblit S. E., Parfenov Yu. V., “Issledovaniya po geomagnetizmu, aeronomii i fizike Solntsa”, Teoreticheskaya fizika, no. 57, Nauka, M., 1981, 83–94; 117–122

[6] Pasquier J., Pasquier R., Nucl. Phys., A277 (1977), 202–220 ; Ann. of Phys., 111 (1978), 269–303 | DOI | DOI

[7] Fuda M. G., Whiting J. S., Phys. Rev., C8 (1973), 1225 | MR

[8] Fuda M. G., Phys. Rev., C14 (1976), 37

[9] Orlov I. I., Parfenov Yu. V., TMF, 4:1 (1970), 18–21 | MR

[10] Korenblit S. E., Zadacha o sdvige urovnei v metode vneenergeticheskikh determinantov Iosta, Preprint 87-16, IYaF SO AN SSSR, Novosibirsk; ЯФ, 49:1 (1989), 197–204 | MR

[11] Gelfand I. M., Shilov G. E., Obobschennye funktsii, vyp. 1, Fizmatgiz, M., 1959 | MR

[12] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii, T. 1, 2, Nauka, M., 1973 | MR

[13] Perelomov A. M., Popov V. S., ZhETF, 50 (1966), 179

[14] Van Haeringen H., van Wageningen R., J. Math. Phys., 16 (1975), 1441 ; Van Haeringen H., J. Math. Phys., 19 (1978), 1379 ; 17 (1976), 997 ; Dusek J., Czech. J. Phys., B31 (1981), 941–968 | DOI | MR | DOI | MR | DOI | MR

[15] Kadyshevskii V. G., Mir-Kasimov R. M., Skachkov N. B., EChAYa, 2:3 (1972), 635–690

[16] Faddeev L. D., Sovremennye problemy matematiki, 3, VINITI, M., 1974, 93–180 | MR

[17] Newton R. C., J. Math. Phys., 23 (1982), 594–604 | DOI | MR

[18] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii, T. 3, Nauka, M., 1967 | MR

[19] Vilenkin N. Ya., Spetsialnye funktsii i teoriya predstavlenii grupp, Nauka, M., 1965 ; Durand L., Fishbane P. M., Simmons L. M., J. Math. Phys., 17 (1976), 1933 | MR | DOI | MR | Zbl

[20] Mandelstam S., Ann. Phys., 21 (1963), 302–343 | DOI | MR | Zbl

[21] Gradshtein I. S., Ryzhik I. M., Tablitsy integralov, summ, ryadov i proizvedenii, Nauka, M., 1971 | MR