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	Dear authors! Submission of all materials is carried out only electronically through Online Submission System in personal account. 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]. ← Contents of issue


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