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Sib. Èlektron. Mat. Izv., 2014, Volume 11, Pages 334–344 (Mi semr491)  

Real, complex and functional analysis

Spectrum and resolvent of a block operator matrix

T. H. Rasulova, I. O. Umarovab

a Bukhara State University
b Самаркандский Профессиональный Колледж Железнодорожного Транспорта, ул. Ибн-Холдун 79, 140102, Самарканд, Узбекистан

Abstract: In the paper the block operator matrix $H$ associated with the system of at most three quantum particles on a $\mathrm{d}$-dimensional lattice is considered. Spectrum of this operator is studied in detail. In particular, it is shown that the operator $H$ has at most four simple eigenvalues lying outside of the essential spectrum. Moreover, the resolvent of $H$ is founded.

Keywords: Block operator matrix, Fock space, annihilation and creation operators, generalized Friedrichs model, Fredholm's determinant, essential and discrete spectrum, resolvent.

Full text: PDF file (528 kB)
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UDC: 517.984
MSC: 81Q10
Received October 29, 2013, published May 16, 2014

Citation: T. H. Rasulov, I. O. Umarova, “Spectrum and resolvent of a block operator matrix”, Sib. Èlektron. Mat. Izv., 11 (2014), 334–344

Citation in format AMSBIB
\Bibitem{RasUma14}
\by T.~H.~Rasulov, I.~O.~Umarova
\paper Spectrum and resolvent of a block operator matrix
\jour Sib. \`Elektron. Mat. Izv.
\yr 2014
\vol 11
\pages 334--344
\mathnet{http://mi.mathnet.ru/semr491}


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