Eigenvalue asymptotics for polynomially compact pseudodifferential operators
Algebra i analiz, Tome 33 (2021) no. 2, pp. 215-232.

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The asymptotics is found for eigenvalues of polynomially compact pseudodifferential operators of the zeroth order.
Keywords: eigenvalue asymptotics, pseudodifferential operators, Neumann–Poincare operator, 3D elasticity.
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G. Rozenblum. Eigenvalue asymptotics for polynomially compact pseudodifferential operators. Algebra i analiz, Tome 33 (2021) no. 2, pp. 215-232. http://geodesic.mathdoc.fr/item/AA_2021_33_2_a8/

[1] Adams M., “Spectral properties of zero order pseudodifferential operators”, J. Funct. Anal., 32:3 (1983), 420–441 | DOI | MR

[2] Agranovich M., Amosov B., Levitin M., “Spectral problems for the Lamé system with spectral parameter in boundary conditions on smooth or nonsmooth boundary”, Russ. J. Math. Phys., 6:5 (1999), 247–281 | MR | Zbl

[3] Ammari H., Ciraolo G., Kang H., Lee H., Milton G., “Spectral theory of a Neumann–Poincaré operator and analysis of cloaking due to anomalous localized resonance”, Arch. Ration. Mech. Anal., 208:2 (2013), 667–692 | DOI | MR | Zbl

[4] Ando K., Kang H., Miyanishi Y., “Elastic Neumann–Poincaré operators in three dimensional smooth domains: polynomial compactness and spectral structure”, Int. Math. Res. Not. IMRN, 2019, no. 12, 3883–3900 | DOI | MR | Zbl

[5] Ando K., Ji Y.-G., Kang H., Kim K., Yu S., “Spectral properties of the Neumann–Poincaré operator and cloaking by anomalous localized resonance for the elasto-static system”, European J. Appl. Math., 29:2 (2018), 189–225 | DOI | MR | Zbl

[6] Birman M. Sh., Solomyak M. Z., “Asimptotika spektrapsevdodifferentsialnykh operatorov s anizotropno-odnorodnymi simvolami”, Vestn. Leningr. un-ta. Ser. mat., mekh., astronom., 1977, no. 3, 13–21 | Zbl

[7] Birman M. Sh., Solomyak M. Z., “Asimptotika spektrapsevdodifferentsialnykh operatorov s anizotropno-odnorodnymi simvolami. II”, Vestn. Leningr. un-ta. Ser. mat., mekh., astronom., 1979, no. 3, 5–10 | Zbl

[8] Birman M. Sh., Solomyak M. Z., “Asimptotika spektra variatsionnykh zadach na resheniyakh ellipticheskikh uravnenii”, Sib. mat. zh., 20:1 (1979), 3–22 | MR | Zbl

[9] Birman M. Sh., Yafaev D. R., “Asimptotika spektra matritsy rasseyaniya”, Zap. nauch. semin. LOMI, 110, 1981, 3–29 | Zbl

[10] Colin de Verdière Y., Saint–Raymond L, “Attractors for two dimensional waves with homogeneous Hamiltonians of degree $0$”, Comm. Pure Appl. Math., 73:2 (2020), 421–462 | DOI | MR | Zbl

[11] Colin de Verdière Y., “Spectral theory of pseudo–differential operators of degree $0$ and application to forced linear waves”, Anal. PDE, 13:5 (2020), 1521–1537 | DOI | MR | Zbl

[12] Deng Y., Li H., Liu H., “On spectral properties of Neuman–Poincaré operator and plasmonic resonances in $3$D elastostatics”, J. Spectral Theory, 9:3 (2019), 767–789 | DOI | MR | Zbl

[13] Duduchava R., Natroshvili D., “Mixed crack type problem in anisotropic elasticity”, Math. Nachr., 191 (1998), 83–107 | DOI | MR | Zbl

[14] Dyatlov S., Zworski M., “Microlocal analysis of forced waves”, Pure Appl. Anal., 1:3 (2019), 359–384 | DOI | MR | Zbl

[15] Grubb G., “Singular Green operators and their spectral asymptotics”, Duke Math. J., 51:3 (1984), 477–528 | DOI | MR | Zbl

[16] Hörmander L., “The spectral function of an elliptic operator”, Acta Math., 121 (1968), 193–218 | DOI | MR | Zbl

[17] Kozhevnikov A., “The basic boundary problems of the static elasticity theory and their Cosserat spectrum”, Math. Z., 213:2 (1993), 241–270 | DOI | MR

[18] Kupradze T. G., Metody potentsiala v teorii uprugosti, FIZMATLIT, M., 1963 | MR

[19] Kupradze T. G., Gegelia T. V., Basheleishvili M. O., Trekhmernye zadachi matematicheskoi teorii uprugosti i termouprugosti, Nauka, M., 1976

[20] Li H., Liu H., “On three–dimensional plasmon resonance in elastostatics”, Ann. Mat. Pura Appl. (4), 196:3 (2017), 1113–1135 | DOI | MR | Zbl

[21] Miyanishi Y., Rozenblum G., Spectral properties of the Neumann–Poincaré operator in 3D elasticity, arXiv: 1904.09449

[22] Tao Z., $0$th Order pseudo-differential operator on the circle, arXiv: 1909.06316

[23] Wang J., The scattering matrix for $0$th order pseudodifferential operators, arXiv: 1909.06484

[24] Yafaev D., “Scattering by magnetic fields”, Algebra i analiz, 17:5 (2005), 244–272 | MR