Djakov, P. B.; Mityagin, B. S. Convergence of spectral decompositions of Hill operators with trigonometric polynomial potentials. (English. Russian original) Zbl 1242.34148 Dokl. Math. 83, No. 1, 5-7 (2011); translation from Dokl. Akad. Nauk 436, No. 1, 11-13 (2011). Spectral decompositions of Hill operators with trigonometric polynomials potentials are analyzed. Conditions for the unconditional convergence of such decompositions are presented. Reviewer: Ioana Dragomirescu (Timisoara) Cited in 16 Documents MSC: 34L10 Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators 34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) Keywords:spectral decompositions; Hill operators; trigonometric polynomials potential PDFBibTeX XMLCite \textit{P. B. Djakov} and \textit{B. S. Mityagin}, Dokl. Math. 83, No. 1, 5--7 (2011; Zbl 1242.34148); translation from Dokl. Akad. Nauk 436, No. 1, 11--13 (2011) Full Text: DOI References: [1] N. Dernek and O. A. Veliev, Israel J. Math. 145, 113–123 (2005). · Zbl 1073.34094 · doi:10.1007/BF02786687 [2] P. Djakov and B. Mityagin, Usp. Mat. Nauk 61(4), 77182 (2006). [3] P. Djakov, B. Mityagin, J. Funct. Anal. 242(1), 157–194 (2007). · Zbl 1115.34079 · doi:10.1016/j.jfa.2006.06.013 [4] P. Djakov and B. Mityagin, Contemp. Math. 481, 59–80 (2009). · doi:10.1090/conm/481/09397 [5] N. Dunford and J. Schwartz, Linear Operators, Part III, Spectral Operators (Wiley, New York, 1971). · Zbl 0243.47001 [6] F. Gesztesy and V. Tkachenko, J. Anal. Math. 107, 287–353 (2009). · Zbl 1193.47037 · doi:10.1007/s11854-009-0012-5 [7] G. M. Keselman, Izv. Vyssh. Uchebn. Zaved. Mat. 39(2), 82–93 (1964). [8] A. S. Makin, Dokl. Akad. Nauk. 406(4), 452–457 (2006). [9] A. S. Makin, Differ. Uravn. 42(12), 1646–1656, (2006). [10] X. R. Mamedov and N. B. Kerimov, Mat. Zamet. 64, 558 563 (1998). [11] V. P. Mikhailov, Dokl. Akad. Nauk SSSR 144, 981–984 (1962). [12] A. Minkin, J. Math. Sci. 96(6), 3631–3715 (1999). · doi:10.1007/BF02172664 [13] A. A. Shkalikov, Uspekhi Mat. Nauk 34, 235–236 (1979). [14] A. A. Shkalikov, Trudy Sem. I. G. Petrovskogo 9, 190–229 (1983). [15] O. A. Veliev, A. A. Shkalikov, Matem. Zamet. 85, 671–686 (2009). · doi:10.4213/mzm6912 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.