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Abstract: We investigate the spectrum of three-dimensional Schrödinger operators with a-interactions of constant strength supported on circular cones. As shown in earlier works, such operators have infinitely many eigenvalues below the threshold of the essential spectrum. We focus on spectral properties for sharp cones, that is when the cone aperture goes to zero, and we describe the asymptotic behavior of the eigenvalues and of the eigenvalue counting function. A part of the results are given in terms of numerical constants appearing as solutions of transcendental equations involving modified Bessel functions.
Fuente: Journal of Mathematical Analysis and Applications, 2018, 458(1), 566-589
Publisher: Academic Press Inc.
Publication date: 01/02/2018
No. of pages: 24
Publication type: Article
DOI: 10.1016/j.jmaa.2017.09.026
ISSN: 0022-247X,1096-0813
Spanish project: MTM2014-53145-P
Publication Url: https://doi.org/10.1016/j.jmaa.2017.09.026
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