M. M. Malamud

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Articles: 6

On the completeness of general boundary value problems for $2 \times 2$ first-order systems of ordinary differential equations

Methods Funct. Anal. Topology 18 (2012), no. 1, 4-18

Let $B={\rm diag} (b_1^{-1}, b_2^{-1}) \not = B^*$ be a $2\times 2$ diagonal matrix with \break $b_1^{-1}b_2 \notin{\Bbb R}$ and let $Q$ be a smooth $2\times 2$ matrix function. Consider the system $$-i B y'+Q(x)y=\lambda y, \; y= {\rm col}(y_1,y_2), \; x\in[0,1],$$ of ordinary differential equations subject to general linear boundary conditions $U_1(y) = U_2(y) = 0.$ We find sufficient conditions on $Q$ and $U_j$ that guaranty completeness of root vector system of the boundary value problem. Moreover, we indicate a condition on $Q$ that leads to a completeness criterion in terms of the linear boundary forms $U_j,\ j\in \{1,2\}.$

Generalized resolvents and boundary triplets for dual pairs of linear relations

Methods Funct. Anal. Topology 11 (2005), no. 2, 170-187

Damir Zyamovich Arov (to the 70th anniversary of his birth)

Methods Funct. Anal. Topology 10 (2004), no. 2, 1-3

Simultaneous similarity of pairs of convolution Volterra operators to fractional powers of the operator of integration

Methods Funct. Anal. Topology 9 (2003), no. 2, 154-162

Krein type formula for canonical resolvents of dual pairs of linear relations

Methods Funct. Anal. Topology 8 (2002), no. 4, 72-100

Generalized resolvents of symmetric operators and admissibility

Methods Funct. Anal. Topology 6 (2000), no. 3, 24-55