Geodesic
Regularized sums of roots of generalized quasipolynomials
Sbornik. Mathematics, Tome 63 (1989) no. 2, pp. 447-455 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A method is given for obtaining formulas for regularized sums of the eigenvalues of a wide class of boundary value problems generated by ordinary differential expressions with a multiple inclusion of the spectral parameter, in the case of multiple roots of the characteristic equation. Bibliography: 15 titles. 
@article{SM_1989_63_2_a11,
     author = {V. A. Lyubishkin},
     title = {Regularized sums of roots of generalized quasipolynomials},
     journal = {Sbornik. Mathematics},
     pages = {447--455},
     year = {1989},
     volume = {63},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1989_63_2_a11/}
}
TY  - JOUR
AU  - V. A. Lyubishkin
TI  - Regularized sums of roots of generalized quasipolynomials
JO  - Sbornik. Mathematics
PY  - 1989
SP  - 447
EP  - 455
VL  - 63
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1989_63_2_a11/
LA  - en
ID  - SM_1989_63_2_a11
ER  - 
%0 Journal Article
%A V. A. Lyubishkin
%T Regularized sums of roots of generalized quasipolynomials
%J Sbornik. Mathematics
%D 1989
%P 447-455
%V 63
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1989_63_2_a11/
%G en
%F SM_1989_63_2_a11
V. A. Lyubishkin. Regularized sums of roots of generalized quasipolynomials. Sbornik. Mathematics, Tome 63 (1989) no. 2, pp. 447-455. http://geodesic.mathdoc.fr/item/SM_1989_63_2_a11/

[1] Gelfand I. M., Levitan B. M., “Ob odnom prostom tozhdestve dlya sobstvennykh znachenii differentsialnogo operatora vtorogo poryadka”, DAN SSSR, 88 (1953), 593–596 | MR

[2] Faddeev L. D., “O vyrazhenii sleda raznosti dvukh singulyarnykh operatorov tipa Shturma–Liuvillya”, DAN SSSR, 115:5 (1957), 878–881 | MR | Zbl

[3] Halberg C. J. A., Kramer V. A., “A generalization of the trace concept”, Duke Math. J., 27:4 (1960), 607–617 | DOI | MR | Zbl

[4] Gasymov M. G., “O summe raznostei sobstvennykh znachenii dvukh samosopryazhennykh operatorov”, DAN SSSR, 150:6 (1963), 1202–1205 | MR | Zbl

[5] Shevchenko R. F., “O slede differentsialnogo operatora”, DAN SSSR, 164:1 (1965), 62–65 | Zbl

[6] Kostyuchenko A. G., O nekotorykh spektralnykh svoistvakh differentsialnykh operatorov, Dis. $\dots$ kand. fiz.-matem. nauk, Izd-vo MGU, M, 1966

[7] Sadovnichii V. A., “O sledakh obyknovennykh differentsialnykh operatorov vysshikh poryadkov”, Matem. sb., 72(114) (1967), 293–317 | Zbl

[8] Lidskii V. B., Sadovnichii V. A., “Regulyarizovannye summy kornei odnogo klassa tselykh funktsii”, Funktsion. analiz i ego pril., 1:2 (1967), 52–59 | MR | Zbl

[9] Lidskii V. B., Sadovnichii V. A., “Asimptoticheskie formuly dlya kornei odnogo klassa tselykh funktsii”, Matem. sb., 75(117) (1968), 558–566 | MR | Zbl

[10] Tamarkin Ya. D., O nekotorykh obschikh zadachakh teorii obyknovennykh lineinykh differentsialnykh uravnenii, Petrograd, 1917 | Zbl

[11] Turritin H. L., “Asymptotic solution of certain ordinary differential equations associated with multiple roots of the characteristic equation”, Amer. J. Math., 58:2 (1936), 364–376 | DOI | MR

[12] Mac Coll L. A., “On the distribution of the zeros of sums of exponentials of polynomials”, Trans. Amer. Math. Soc., 36 (1934), 341–360 | DOI | MR | Zbl

[13] Turrittin H. L., “Asymptotic distribution of zeros for certain exponential sums”, Amer. J. Math., 66 (1944), 199–228 | DOI | MR | Zbl

[14] Sadovnichii V. A., Lyubishkin V. A., Belabbasi Yu., “O regulyarizovannykh summakh kornei tseloi funktsii odnogo klassa”, DAN SSSR, 254:6 (1980), 1346–1348 | MR

[15] Sadovnichii V. A., Lyubishkin V. A., “Regulyarizovannye summy kornei odnogo klassa tselykh funktsii eksponentsialnogo tipa”, DAN SSSR, 256:4 (1981), 794–798 | MR