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

A. V. Agibalova, M. M. Malamud, L. L. Oridoroga

↓ Abstract   |   Article (.pdf)

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

Seppo Hassi, Mark Malamud, Vadim Mogilevskii

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

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

V. M. Adamyan, Yu. M. Berezansky, M. L. Gorbachuk, V. I. Gorbachuk, G. M. Gubreev, A. N. Kochubei, M. M. Malamud

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

Mark M. Malamud, Rob Zuidwijk

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

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

M. M. Malamud, V. I. Mogilevskii

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

Generalized resolvents of symmetric operators and admissibility

H. S. V. de Snoo, V. A. Derkach, S. Hassi, M. M. Malamud

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

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