Geodesic
Semibounded local hamiltonians for perturbations of the laplacian supported by curves with angle points in $\mathbb R^4$
Teoretičeskaâ i matematičeskaâ fizika, Tome 106 (1996) no. 2, pp. 179-199 
Yu. G. Shondin. Semibounded local hamiltonians for perturbations of the laplacian supported by curves with angle points in $\mathbb R^4$. Teoretičeskaâ i matematičeskaâ fizika, Tome 106 (1996) no. 2, pp. 179-199. http://geodesic.mathdoc.fr/item/TMF_1996_106_2_a0/
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     title = {Semibounded local hamiltonians for perturbations of the laplacian supported by curves with angle points in~$\mathbb R^4$},
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     url = {http://geodesic.mathdoc.fr/item/TMF_1996_106_2_a0/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Perturbations supported by curves with angle points are studied for the Laplacian in $\mathbb R^4$ within the framework of the extension theory. Classes of the self-adjoint extensions that are local, semibounded and generate a positivity preserving semigroup are distinguished. Their connection with the local Dirichlet forms is obtained.

[1] Shondin Yu. G., TMF, 105:1 (1995), 3–17 | MR | Zbl

[2] Pavlov B. S., UMN, 42:6 (1987), 99–131 | MR

[3] Shondin Yu. G., TMF, 51:2 (1982), 181–191 | MR

[4] Thomas L. E., Phys. Rev., D30:6 (1984), 1233–1236

[5] Pavlov B. S., Matem. sb., 136:2 (1988), 163–177 | Zbl

[6] Makarov K. A., Algebra i analiz, 4:5 (1992), 155–171 | MR

[7] Khepp K., Teoriya perenormirovok, Nauka, M., 1974 | MR

[8] Shondin Yu. G., TMF, 92:3 (1992), 466–472 | MR | Zbl

[9] Albeverio S., Høegh-Krohn R., Streit L., J. Math. Phys., 18:5 (1977), 907–917 | DOI | MR | Zbl

[10] Fukushima M., Dirichlet Forms and Markov Processes, North-Holland, Amsterdam, 1980 | MR

[11] Albeverio S., Gestezi F., Kheeg-Kron R., Kholden Kh., Reshaemye modeli v kvantovoi mekhanike, Mir, M., 1991 | MR

[12] Venttsel A. D., Teor. veroyatn. i ee prilozh., 4:2 (1959), 172–185 | MR | Zbl

[13] Vatanabe S., Ikeda N., Stokhasticheskie differentsialnye uravneniya i diffuzionnye protsessy, Nauka, M., 1986 | MR

[14] Birman M. Sh., Matem. sb., 38:4 (1956), 431–450 | MR | Zbl

[15] Derkach V. A., Malamud M. M., J. Funct. Anal., 95:1 (1991), 1–95 | DOI | MR | Zbl

[16] Malamud M. M., DAN USSR. Ser. A, 1990, no. 3, 20–25 | MR | Zbl

[17] Alonso A., Simon B., J. Oper. Theory, 4 (1980), 251–270 | MR | Zbl

[18] Rid M., Saimon B., Metody sovremennoi matematicheskoi fiziki. T. IV. Analiz operatorov, Mir, M., 1982 | MR

[19] Brasche J., Perturbations of self-adjoint operators supported by null sets, Dissertation, Bielefeld, 1988 | Zbl