×
Bahri, S. M.

Carleman integral operators as multiplication operators and perturbation theory. (English) Zbl 1488.45057

Kragujevac J. Math. 41, No. 1, 71-80 (2017).
Summary: In this paper we introduce a multiplication operation that allows us to give to the Carleman integral operator of second class [S. M. Bahri, Z. Anal. Anwend. 26, No. 1, 57–64 (2007; Zbl 1142.47027); T. Carleman, Sur les équations intégrales singulières à noyau réel et symétrique (French). Uppsala: Uppsala Almquwist Wiksells Boktryckeri (1923; JFM 49.0272.01)] the form of a multiplication operator. Also we establish the formaly theory of perturbation of such operators.

MSC:

45P05 Integral operators
47G10 Integral operators

Keywords:

Carleman kernel; defect indices; integral operator; formal series

Citations:

Zbl 1142.47027; JFM 49.0272.01
Cite Review PDF
Full Text: Link

References:

[1] M. B. Abrahamse,Multiplication operators, Lecture Notes in Mathematics693(1993), 17-36. · Zbl 0411.47021
[2] N. I. Akhiezer and I. M. Glazman,Theory of Linear Operators in Hilbert Space, Dover Books on Mathematics, Dover Publications, New York, 1993. · Zbl 0874.47001
[3] S. M. Bahri,On the extension of a certain class of Carleman operators, Z. Anal. Anwend.26 (2007), 57-64. · Zbl 1142.47027
[4] S. M. Bahri,Spectral properties of a certain class of Carleman operators, Arch. Math. (Brno) 43(2007), 163-175. · Zbl 1164.05037
[5] S. M. Bahri,On convex hull of orthogonal scalar spectral functions of a Carleman operator, Bol. Soc. Parana. Mat. (3)26(1-2) (2008), 9-18. · Zbl 1178.45019
[6] S. M. Bahri,On the localization of the spectrum for quasi-selfadjoint extensions of a Carleman operator, Math. Bohem.137(2012), 249-258. · Zbl 1265.45001
[7] M. K. Belbahri,Series de Laurent formelles, Office des Publications Universitaires, Alger, 1981.
[8] T. Carleman,Sur les Equations Intégrales Singulières à Noyau Réel et Symétrique, Uppsala Almquwist Wiksells Boktryckeri, Uppsala, 1923. · JFM 49.0272.01
[9] V. B. Korotkov,Integral Operators with Carleman Kernels (in Russian), Nauka, Novosibirsk, 1983. · Zbl 0186.20601
[10] G. I. Tagronski,On Carleman integral operators, Proc. Amer. Math. Soc.18(1967), 450-456. · Zbl 0147.12002
[11] J. Weidman,Carleman operators, Manuscripts Math.2(1970), 1-38. · Zbl 0185.20401
[12] J. Weidman,Linear Operators in Hilbert Spaces, Spring Verlag, New-York Heidelberg Berlin, 1980. · Zbl 0434.47001
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.