@article{3618bdb6e4d64b579bff93fedc1a72c3,

title = "Fold completeness of a system of root vectors of a system of unbounded polynomial operator pencils in Banach spaces. I. Abstract theory",

abstract = "N. Dunford and J.T. Schwartz (1963) striking Hilbert space theory about completeness of a system of root vectors (generalized eigenvectors) of an unbounded operator has been generalized by J. Burgoyne (1995) to the Banach spaces framework. We use the Burgoyne's theorem and prove n-fold completeness of a system of root vectors of a system of unbounded polynomial operator pencils in Banach spaces. The theory will allow to consider, in application, boundary value problems for ODEs and elliptic PDEs which polynomially depend on the spectral parameter in both the equation and the boundary conditions.",

keywords = "Approximation numbers, Discrete spectrum, Fold completeness, Gelfand numbers",

author = "Yakov Yakubov",

note = "Funding Information: E-mail address:

[email protected]. URL: http://www.math.tau.ac.il/~yakubov. 1 The author was supported by the Israel Ministry of Absorption.",

year = "2009",

month = sep,

doi = "10.1016/j.matpur.2009.04.005",

language = "אנגלית",

volume = "92",

pages = "263--275",

journal = "Journal des Mathematiques Pures et Appliquees",

issn = "0021-7824",

publisher = "Elsevier Masson SAS",

number = "3",

}