Abstract
We formulate three open questions related to enumerative combinatorics, which arise in the spectral analysis of Hill operators with trigonometric polynomial potentials.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Djakov P., Mityagin B.: Asymptotics of instability zones of the Hill operator with a two term potential. J. Funct. Anal 242(1), 157–194 (2007)
Djakov P., Mityagin B.: Convergence of spectral decompositions of Hill operators with trigonometric polynomial potentials. Math. Ann. 351, 509–540 (2011)
Borwein J.M., Straub A., Wan J., Zudilin W.: Densities of short uniform random walks (with an appendix by D. Zagier). Can. J. Math. 64(5), 961–990 (2012) arXiv:1103.2995v2
Edelman, A., Kostlan, E.: The road from Kac’s matrix to Kac’s random polynomials. In: Proceedings of the Fifth SIAM Conference on Applied Linear Algebra, Philadelphia, pp. 503–507 (1994)
Rosenberg, S.: On a combinatorial Identity of Djakov and Mityagin. arXiv:1205.6236, 28 May 2012
Taussky O., Todd B.: Another look at a matrix of Mark Kac. Linear Algebra Appl. 150, 341–360 (1991)
van Lint J.H., Wilson R.M.: A Course in Combinatorics. Cambridge University Press, Cambridge (1992)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Djakov, P., Mityagin, B. Combinatorial Identities Related to Eigen-Function Decompositions of Hill operators: Open Questions. Integr. Equ. Oper. Theory 75, 7–12 (2013). https://doi.org/10.1007/s00020-012-2016-2
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00020-012-2016-2