Paired Integral Operators with Homogeneous-Difference Kernels

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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.2016.2.5913 Paired Integral Operators with Homogeneous-Difference Kernels Avsyankin O. G. Vladikavkaz Mathematical Journal 2016. Vol. 18. Issue 2. Abstract: We consider the paired multidimensional integral operators with homogeneous-difference kernels, acting in \(L_p\)-spaces. For these operators the symbol is defined. In term of the symbol the necessary and sufficient conditions for the invertibility of operators are obtained. Keywords: integral operator, homogeneous-difference kernel, symbol, invertibility, spherical harmonics. Language: Russian Download the full text For citation: Avsyankin O. G. Paired integral operators with homogeneous-difference kernels // Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 19, no. 2, pp. 3-11. DOI 10.23671/VNC.2016.2.5913 + References 1. Karapetiants N., Samko S. Equations with Involutive Operators. Birkhauser, Boston-Basel-Berlin, 2001. 427 p. 2. Avsyankin O. G. On the C-algebra Generated by Multidimensional Integral Operators with Homogeneous Kernels and Multiplicative Translations. Doklady RAN [Doklady Mathematics], 2008, vol. 77, no. 2, pp. 298-299 [in Russian]. 3. Avsyankin O. G., Peretyat'kin F. G. Boundedness and Compactness of Multidimensional Integral Operators with Homogeneous Kernels. Russian Mathematics, 2013, vol. 57, no. 11, pp. 57-60. 4. Avsyankin O. G. Projection Method for Integral Operators with Homogeneous Kernels Perturbed by One-sided Multiplicative Shifts. Russian Mathematics, 2015, vol. 59, no. 2, pp. 7-13. 5. Avsyankin O. G. Multidimensional Integral Operators with Homogeneous-Difference Kernels. Differential Equations, 2012, vol. 48, no. 1, pp. 65-71. 6. Avsyankin O. G. On an Algebra of Multidimensional Integral Operators with Homogeneous-Difference Kernels. Mathematical Notes, 2014, vol. 95, no. 1, pp. 141-146. 7. Samko S. G. Gipersinguljarnye integraly i ih prilozhenija* [Hypersingular Integrals and Their Applications]. Rostov-on-Don, RSU, 1984. 208 p. [in Russian]. 8. Simonenko I. B. Operators of Convolution Type in Cones. Mathematics of the USSR-Sbornik, 1967, vol. 3, no. 2, pp. 279-293. 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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