# M. I. Muminov

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Articles: 2

### The Faddeev equation and essential spectrum of a Hamiltonian in Fock space

Methods Funct. Anal. Topology 17 (2011), no. 1, 47-57

A Hamiltonian (model operator) $H$ associated to a quantum system describing three particles in interaction, without conservation of the number of particles, is considered. The Faddeev type system of equations for eigenvectors of $H$ is constructed. The essential spectrum of $H$ is described by the spectrum of the channel operator.

### On the spectrum of a model operator in Fock space

Methods Funct. Anal. Topology 15 (2009), no. 4, 369-383

A model operator $H$ associated to a system describing four particles in interaction, without conservation of the number of particles, is considered. We describe the essential spectrum of $H$ by the spectrum of the channel operators and prove the Hunziker-van Winter-Zhislin (HWZ) theorem for the operator $H.$ We also give some variational principles for boundaries of the essential spectrum and interior eigenvalues.