Linear relations as generators of semigroups of operators

Spectral analysis of differential operators with unbounded operator coefficients on the half-line

“…The notions of the theory of linear relations (multivalued linear operators) presented and used below can be found in the papers [2,6,[15][16][17][18] and the monograph [19, pp. 6-9].…”

“…(3). In this case, a necessary and sufficient condition for the continuous invertibility of the operator L E is the exponential decay of the family U of evolutionary operators, i.e., the condition that U (t, s) ≤ Ce −β(t−s) , s ≤ t, for some C ≥ 1 and β > 0 (see [1,2,[4][5][6][7]). In the special case where the operators A(t), t ≥ 0, in Eq.…”

On the essential spectra of some matrix of linear relations

“…The investigation of spectral (especially the theory of the essential spectra) theory of linear relations has important applications to several problems of operator theory. We cite some of them [3][4][5][6][7][8][9][10]. First, the spectral theory of ordered pair of operators.…”

On uniqueness of fractional powers of multi-valued linear operators and the incomplete Cauchy problem

“…In [7], a wide coverage of general issues of the theory of this kind of operator could be found. For applications of multi-valued methods to the study of degenerate differential equations, we refer to the monograph [11] (see also [17,Section 6.1]; for more recent studies in the same direction see [3][4][5][6]12]). …”