On Partially Measure Compact Unbounded Linear Operators on \(L_2\)

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Home Editorial board Publication ethics Peer review guidelines Latest issue All issues Rules for authors Online submission system's guidelines Submit manuscript Contacts Address: Vatutina st. 53, Vladikavkaz, 362025, RNO-A, Russia Phone: (8672)23-00-54 E-mail: rio@smath.ru	DOI: 10.23671/VNC.2016.1.5947 On Partially Measure Compact Unbounded Linear Operators on \(L_2\) Korotkov V. B. Vladikavkaz Mathematical Journal 2016. Vol. 18. Issue 1. Abstract: In this paper we introduce partially measure compact unbounded linear operators. We find characteristic property of limit spectrums of the adjoints of unbounded densely defined partially measure compact linear operators on \(L_2(\mu)\). Some applications of this result to linear functional equations of the first and second kind with partially measure compact unbounded operators are given. Keywords: closed operator, measure compact operator, limit spectrum, linear functional equations of the first and second kind, linear integral equations of the first and second kind Language: Russian Download the full text For citation: Korotkov V. B. On partially measure compact unbounded linear operators on \(L_2\) // Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 19, no. 1, pp. 36-41. DOI 10.23671/VNC.2016.1.5947 + References 1. Kato T. Perturbation Theory for Linear Operators. Berlin - Heidelberg - New-York, Springer-Verlag, 1966. 2. Krasnosel'skii M.A., Zabreiko P.P., Pustyl'nik E.I., and Sobolevskii P.E. Integral Operatorsin Spaces of Summable Functions. Leyden, Noordhoff Internat. Publ., 1976. 3. Aronszajn N., Szeptycki P. On General Integral Transformations, Math. Ann., 1966, vol.163, no.2, pp. 127-154. 4. Korotkov V.B. Integral'nye operatory [Integral Operators]. Nobosibirsk, Nauka, 1983 [in Russian]. 5. Korotkov V.B. O privedenii semejstv operatorov k integral'nomu vidu [On reduction of families of operators to integral form]. Sibirskij Mat. Zh. [Sib. Math. Zh.], 2006, vol.47, no.5, pp.1092-1098 [in Russian]. 6. Korotkov V.B. and Stepanov V.D. Kriterii porozhdaemosti integral'nyh operatorov izmerimymi funkcijami [Criterions of generaly of integral operators by measurable functions]. Sibirskij Mat. Zh. [Sib. Math. Zh.], 1982, vol.23, no.2, pp.199-203 [in Russian]. 7. Korotkov V.B. Nekotorye voprosy teorii integral'nyh operatorov [Some Topics in the Theory of Integral Operators]. Nobosibirsk, SO AN SSSR, 1988 [in Russian]. 8. Verlan' A.F., Sizikov V.S. Integral'nye uravnenija: metody, algoritmy, programmy [Integral Equations: Methods, Algoritms, Programms]. Kiev, Naukova dumka, 1986 [in Russian]. The sole copyright holder of the published work is the Founder of the Vladikavkaz Mathematical Journal. The terms of use of this work are governed by an open license (Creative Commons Attribution-NonCommercial 4.0 International). The use of metadata of the scientific article, including the title, abstract, author information, references, identifiers, and other bibliographic description elements for subsequent unrestricted use, is carried out under the terms of the CC BY or CC0 open licenses. ← Contents of issue


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