Separating functions and their applications
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 14, Tome 338 (2006), pp. 202-212 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the present paper the survey of applications of separating functions in the theory of representations of quivers and algebras in linear and metric spaces is given. Application of these functions to the problems of spectral graph theory is also demonstrated.
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I. K. Redchuk. Separating functions and their applications. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 14, Tome 338 (2006), pp. 202-212. http://geodesic.mathdoc.fr/item/ZNSL_2006_338_a8/

[1] L. A. Nazarova, A. V. Roiter, “Norma otnosheniya, razdelyayuschie funktsii i predstavleniya markirovannykh kolchanov”, Ukr. mat. zhurn., 54:6 (2002), 18–54 | MR

[2] L. A. Nazarova, A. V. Roiter, “Konechnopredstavimye diadicheskie mnozhestva”, Ukr. mat. zhurn., 52:6 (2000), 1363–1396 | MR | Zbl

[3] K. I. Belousov, L. A. Nazarova, A. V. Roiter, “Konechno-predstavimye triadicheskie mnozhestva”, Algebra i analiz, 9:4 (1997), 3–27 | MR | Zbl

[4] A. V. Roiter, “The norm of a relation”, Representation Theory I. Finite Dimensional Algebras, Proc. Ottawa, 1984, Lect. Notes in Math., 1177, Springer, Berlin, 1984, 269–272 | MR

[5] M. M. Kleiner, “Chastichno uporyadochennye mnozhestva konechnogo tipa”, Issledovaniya po teorii predstavlenii, Zap. nauchn. semin. LOMI, 28, 1972, 32–41 | MR | Zbl

[6] L. A. Nazarova, “Chastichno uporyadochennye mnozhestva beskonechnogo tipa”, Izv. AN SSSR, Ser. matem., 39 (1975), 963–991 | MR | Zbl

[7] L. A. Nazarova, A. V. Roiter, M. N. Smirnova, “Antimonotonnye i $P$-tochnye kvadratichnye formy i predstavleniya chastichno uporyadochennykh mnozhestv”, Algebra i analiz, 17:6 (2005), 161–183 | MR

[8] N. Burbaki, Gruppy Li i algebry Li, Glavy IV–VI, Mir, M., 1972, 331 pp. | Zbl

[9] A. Möbius A., “Theorie der symmetrischen Figuren”, Gessammelte Werke, t. II, Hirzel, Leipzig, 1886, 561–708

[10] A. V. Roiter, “Representations of marked quivers”, Publ. House Beijing Normal Univ., 2 (2001), 417–423 | MR

[11] P. Gabriel, “Unzerlegbare Darstellungen, I”, Manuscripta Math., 6 (1972), 71–103 | DOI | MR | Zbl

[12] M. A. Vlasenko, A. S. Mellit, Yu. S. Samoilenko, “Ob algebrakh, porozhdennykh lineino svyazannymi obrazuyuschimi s zadannym spektrom”, Funkts. analiz i prilozh., 39:3 (2005), 14–27 | MR | Zbl

[13] S. A. Kruglyak, V. I. Rabanovich, Yu. S. Samoilenko, “O summakh proektorov”, Funkts. analiz i prilozh., 36:3 (2002), 20–35 | MR | Zbl

[14] I. K. Redchuk, “Razdelyayuschie funktsii, spektralnaya teoriya grafov i lokalno-skalyarnye predstavleniya v gilbertovykh prostranstvakh”, Ukr. Mat. Zhur., 58:1 (2006), 36–46 | MR | Zbl

[15] I. K. Redchuk, A. V. Roiter, “Singulyarnye lokalno-skalyarnye predstavleniya kolchanov v gilbertovykh prostranstvakh i razdelyayuschie funktsii”, Ukr. Mat. Zhur., 56:6 (2004), 796–809 | MR | Zbl

[16] S. A. Kruglyak, A. V. Roiter, “Lokalno-skalyarnye predstavleniya grafov v kategorii gilbertovykh prostranstv”, Funkts. analiz i pril., 39:2 (2005), 13–30 | MR | Zbl

[17] V. G. Kac, “Infinite root systems, representations of graphs and invariant theory, II”, J. Algebra, 78 (1982), 141–162 | DOI | MR | Zbl

[18] S. Albeverio, V. Ostrovskyi, Yu. Samoilenko, “On functions on graphs and representations of a certain class of $*$-algebras”, J. of Algebra, in press | MR

[19] D. Cvetkovic, M. Doob, H. Sachs, Spectra of graphs, Academic Press, New York, 1979, 368 pp. | MR

[20] F. Harary, A. J. Schwenk, “Which graphs have integral spectra?”, Graphs and Combinatorics, Springer-Verlag, Berlin–Heidelberg–New York, 1974, 45–51 | MR

[21] F. C. Bussemaker, D. Cvetkovic, “There are exactly 13 connected, cubic, integral graphs”, Univ. Beograd Publ. Elektotehn. Fak., Ser. Mat. Fiz., 1976, no. 544–576, 43–48 | MR

[22] D. Cvetkovic, I. Gutman, N. Trinajstic, “Conjugated molecules having integrtal graph specrta”, Chem Phys. Letters, 29 (1974), 65–68 | DOI

[23] M. Capobianco, S. Maurer, D. McCarthy, J. Molluzzo, “A colection of open problems”, Ann. New York Acad. Sci., 1980, 582–583 | MR

[24] X. L. Li, L. G. Wang, “Integral trees – a survey”, Chinese J. Eng. Math., 17 (2000), 91–93, 96

[25] L. G. Wang, X. L. Li, “Integral trees with diameter 5, 6”, Discrete Math., 297 (2005), 128–143 | DOI | MR | Zbl

[26] M. Watanabe, A. J. Schwenk, “Integral starlike trees”, J. Austral. Math. Soc., Ser. A, 28:1 (1979), 120–128 | DOI | MR | Zbl