×

Stable continuous spectra for differential operators of arbitrary order. (English) Zbl 1089.35036

The authors deal with integral operators with general integral conditions for the kernels. Bounded functions are involved of operators whose continuous, absolutely continuous and the singular continuous spectra coincide. The abstract results are applied for an operator \(H_0\) given by a polyharmonic or fractional Laplacian. Another operator \(H\) is given as a perturbation of \(H_0\), where perturbations are allowed by variable coefficients, potentials or obstacles.

MSC:

35P05 General topics in linear spectral theory for PDEs
35P25 Scattering theory for PDEs
47A10 Spectrum, resolvent
47A40 Scattering theory of linear operators
47F05 General theory of partial differential operators
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Barbatis G., J. Operator Theory 36 pp 179–
[2] DOI: 10.1007/978-3-0348-5440-5 · doi:10.1007/978-3-0348-5440-5
[3] Bertoin J., Lévy Processes (1996)
[4] Birman M. Sh., Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 171 pp 12–
[5] DOI: 10.1007/978-3-642-57856-4 · Zbl 0819.60068 · doi:10.1007/978-3-642-57856-4
[6] Cycon H. L., Text and Monographs in Physics, in: SchrÖdinger Operators with Application to Quantum Mechanics and Global Geometry (1987)
[7] DOI: 10.1006/jfan.1995.1103 · Zbl 0839.35034 · doi:10.1006/jfan.1995.1103
[8] DOI: 10.1023/A:1009888025760 · Zbl 0954.47003 · doi:10.1023/A:1009888025760
[9] DOI: 10.1007/BF01197534 · Zbl 0842.47013 · doi:10.1007/BF01197534
[10] DOI: 10.1007/978-3-0348-8460-0 · doi:10.1007/978-3-0348-8460-0
[11] DOI: 10.1007/BF01940771 · Zbl 0389.47005 · doi:10.1007/BF01940771
[12] DOI: 10.1016/0003-4916(79)90252-5 · Zbl 0408.47009 · doi:10.1016/0003-4916(79)90252-5
[13] DOI: 10.1515/9783110889741 · doi:10.1515/9783110889741
[14] Giere E., Math. Nachr. 263 pp 133–
[15] Hawkes J., Proc. London Math. Soc. 38 pp 335–
[16] Herbst I. W., Trans. Amer. Math. Soc. 236 pp 325–
[17] Muthuramalingam P., Ann. Sci. École. Norm. Sup. 18 pp 57– · Zbl 0584.47009 · doi:10.24033/asens.1484
[18] Perry P. A., Scattering Theory by the Enss Method (1983) · Zbl 0529.35004
[19] Reed M., Methods of Modern Mathematical Physics III, Scattering Theory (1979) · Zbl 0405.47007
[20] Sato K.-I., Lévy Processes and Infinitely Divisible Distributions (1999) · Zbl 0973.60001
[21] DOI: 10.1090/S0273-0979-1982-15041-8 · Zbl 0524.35002 · doi:10.1090/S0273-0979-1982-15041-8
[22] DOI: 10.1215/S0012-7094-79-04607-6 · Zbl 0402.35076 · doi:10.1215/S0012-7094-79-04607-6
[23] DOI: 10.1006/jfan.1994.1054 · Zbl 0803.47015 · doi:10.1006/jfan.1994.1054
[24] DOI: 10.1007/978-3-662-11281-6 · doi:10.1007/978-3-662-11281-6
[25] DOI: 10.1023/A:1010918505818 · Zbl 0988.35176 · doi:10.1023/A:1010918505818
[26] Yafaev D. R., Mat. Zametki 15 pp 445–
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.