MATHEMATICA BOHEMICA, Vol. 137, No. 3, pp. 249-258, 2012

On the localization of the spectrum for quasi-selfadjoint extensions of a Carleman operator

S. M. Bahri

S. M. Bahri, LMPA, Department of Mathematics, Abdelhamid Ibn Badis University of Mostaganem, PB 227, Mostaganem, 27000, Algeria, e-mail: bahrisidimohamed@univ-mosta.dz; bahrisidimohamed@yahoo.fr

Abstract: In the present work, using a formula describing all scalar spectral functions of a Carleman operator $A$ of defect indices $( 1,1) $ in the Hilbert space $L^2( X,\mu) $ that we obtained in a previous paper, we derive certain results concerning the localization of the spectrum of quasi-selfadjoint extensions of the operator $A$.

Keywords: defect indices, integral operator, quasi-selfadjoint extension, spectral theory

Classification (MSC 2010): 45P05, 47B25, 58C40

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