# 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

Let A be a symmetric linear operator (or relation) with equal, possibly infinite, defect numbers. It is well know that one can associate with A a boundary value space and the Weyl function M(λ). The authors show that certain fractional-linear transforms of M(λ) are identified as Weyl functions of extensions of A, and vice versa. This connection is applied to various problems arising in the extension theory of symmetric operators. Some new criteria for a linear operator to be selfadjoint are established. When the defect numbers of A are finite the structure of all selfadjoint extensions with an exit space is completely characterized via a pair of boundary value spaces and their respective Weyl functions. New admissibility criteria are given which guarantee that a generalized resolvent of a nondensely defined symmetric operator corresponds to a selfadjoint operator extension.