×

Some properties of eigenvalues of the Schrödinger operator. (English. Russian original) Zbl 0697.35118

J. Sov. Math. 42, No. 3, 1720-1722 (1988); translation from Issled. Prikl. Mat. 5, 105-110 (1976).
The small-time asymptotics of the diagonal of the heat kernel are computed by stochastic methods. This gives information about the second term in the high energy asymptotics of the level counting function.

MSC:

35Q99 Partial differential equations of mathematical physics and other areas of application
35P25 Scattering theory for PDEs
81P20 Stochastic mechanics (including stochastic electrodynamics)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] R. A. Aleksandryan, V. A. Berezanskii, V. A. Il’in, and A. G. Kostyuchenko, ?Some issues of spectral theory for partial differential equations,? in: Partial Differential Equations [in Russian], Nauka, Moscow (1970).
[2] M. Kac, ?Can one hear the shape of a drum?? Am. Math. Mon.,73, No. 4, Part II, 1?23 (1966). · Zbl 0139.05603 · doi:10.2307/2313748
[3] D. Ray, ?On spectra of second-order differential operators,? Trans. Am. Math. Soc.,77, 299?321 (1954). · doi:10.1090/S0002-9947-1954-0066539-2
[4] E. A. Begovatov, ?On the construction of Green’s function of the heat conduction equation for some boundary-value problems,? Uch. Zap. Kazan Univ.,127, No. 3, 3?6 (1967).
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.