caa a22 4500 60552520X CHVBK 20210128100757.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s10958-015-2480-8 doi (NATIONALLICENCE)springer-10.1007/s10958-015-2480-8 Tsikhistavi Z. Georgian Technical University, Tbilisi, Georgia aut On the Asymptotic Distribution of a Spectrum of Polynomial Bundles of Differential Operators [Elektronische Daten] [Z. Tsikhistavi] We study the asymptotic distribution of eigenvalues of polynomial operator bundles, i.e., of operator polynomials P(z) = P0 + zP1 + · · · zmPm, where z is a spectral parameter and Pj , j = 0, 1, . . . ,m, are linear operators in the Hilbert space . Problems on eigenvalues considered on a closed manifold and in a bounded domain of the Euclidean space lead to bundles of the form P(z) = P0 + zP1 + · · · zmPm with unbounded coefficients such that the asymptotic behavior of their eigenvalues is defined by all operators Pk, k = 0, 1, . . . ,m. We describe classes of bundles whose eigenvalues tend to infinity on a complex plane along a finite number of rays coming out from the origin. Thus the set of all eigenvalues can be partitioned into a finite number of series depending on the ray along which they tend to infinity. Separately for each series, we obtain the main term of the asymptotics of the corresponding function of distribution of eigenvalues. Also, the asymptotic behavior of a spectrum of square bundles arising as a result of separation of variables in the equilibrium problem for an elastic semi-cylinder is studied. Springer Science+Business Media New York, 2015 Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 208/6(2015-08-01), 723-758 1072-3374 208:6<723 2015 208 10958 https://doi.org/10.1007/s10958-015-2480-8 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10958-015-2480-8 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Tsikhistavi Z. Georgian Technical University, Tbilisi, Georgia aut NATIONALLICENCE 773 0- Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 208/6(2015-08-01), 723-758 1072-3374 208:6<723 2015 208 10958