Bahri, S. M. On the extension of a certain class of Carleman operators. (English) Zbl 1142.47027 Z. Anal. Anwend. 26, No. 1, 57-64 (2007). The integral operators of Carleman play an important role in the spectral theory of selfadjoint operators and are the object of several works such those of G.I.Targonski [Proc.Am.Math.Soc.18, 450–456 (1967; Zbl 0147.12002)], V.B.Korotkov [Sib.Math.J.11,(1) (1970)], and J.Weidmann [Manuscr.Math.2, 1–38 (1970; Zbl 0185.20401)].In the present paper, the author study a certain class of those operators in the Hilbert space \(L^2(X,\mu)\). More precisely, the author give necessary and sufficient conditions so that they possess equal deficiency indices. Such operators find their applications in the theory of random variable approximation. Reviewer: Kun Soo Chang (Seoul) Cited in 1 ReviewCited in 1 Document MSC: 47G10 Integral operators 47B25 Linear symmetric and selfadjoint operators (unbounded) 47B38 Linear operators on function spaces (general) Keywords:deficiency indices; integral operator; Carleman kernel Citations:Zbl 0185.20401; Zbl 0147.12002 × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Akhiezer, N. I. and Glazman, I. M., Theory of Linear Operators in Hilbert Space. New York: Dover 1993. · Zbl 0098.30702 [2] Buchwalter, H. and Tarral, D., Théorie Spectrale (in French). Lyon: Publ. Dép. Math. 8/C 1982. · Zbl 0532.47014 [3] Carleman, T., Sur les équations intégrales singuli‘eres ‘ a noyau réel et symé- trique (in French). Uppsala: Uppsala Almquwist Wiksells Boktryckeri 1923. · JFM 49.0272.01 [4] Chatterji, S. D., Cours d’analyse T3. Bienne: Presses Polytechn. Univ. Ro- mandes 1998. [5] Korotkov, V. B., On characteristic properties of Carleman operators (in Rus- sian). Sib. Math. J. 11 (1970)(1), 103 - 127. [6] Targonski, G. I., On Carleman integral operators. Proc. Amer. Math. Soc. 18 (1967)(3), 450 - 456. · Zbl 0147.12002 · doi:10.2307/2035476 [7] Weidmann, J., Carlemanoperatoren (in German). Manuscripta Math. 2 (1970), 1 - 38. · Zbl 0185.20401 · doi:10.1007/BF01168477 [8] Weidmann, J., Linear Operators in Hilbert Spaces. New York: Springer 1980. · Zbl 0972.47002 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.