THE ESSENTIAL SPECTRUM OF THE SCHRÖDINGER OPERATOR FOR A THREE-PARTICLE SYSTEM WITH MASSES 𝒎𝟏 = 𝒎𝟐 = ∞ AND 𝒎𝟑 < ∞

We consider a family of parameter-dependent discrete Schrödinger operators corresponding to the Hamiltonian of a system of three arbitrary particles (either fermions or bosons) with masses 𝑚ଵ = 𝑚ଶ = ∞ and 𝑚ଷ < ∞, on the integer lattice, ℤ ଷ. The interactions of particles are described via zero-range attractive forces. Using the direct-integral decomposition method, the threeparticle problem is reduced to the study of simpler two-particle Schrödinger operators, called the channel (or fiber) operators. Using the channel operators, we find that the essential spectrum consists of a finite union of real segments.