A convergence criterion of a smoothing method for singular integral operators with piecewise continuous coefficients

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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.2014.4.10262 A convergence criterion of a smoothing method for singular integral operators with piecewise continuous coefficients Pilidi V. S. Vladikavkaz Mathematical Journal 2014. Vol. 16. Issue 4. Abstract: For a complete singular integral operator with piecewise continuous coefficients on the real axis a criterion of convergence of an approximation method by a family of complete singular integral operators with the coefficients being continuous on the one-point compactification of the real axis is obtained. Keywords: complete singular integral operator, piecewise continuous coefficients, convergence of the approximation method, uniform invertibility, local principle Language: Russian Download the full text For citation: Pilidi V. S. A convergence criterion of a smoothing method for singular integral operators with piecewise continuous coefficients // Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 16, no. 4, pp. 54-60. DOI 10.23671/VNC.2014.4.10262 + References 1. Gohberg I. C., Fel'dman I. A. Uravnenija v Svertkah i Proekcionnye Metody ih Reshenija, Moskva, Nauka, 1971, 432 p. (Russian). 2. Pilidi V. S. Obosnovanie metoda sglazhivanija kojefficientov dlja singuljarnyh integral'nyh operatorov s kusochno-nepreryvnymi kojefficientami. Izv. Vysshih Uchebnyh Zavedenij. Sev.-Kavk. Reg., 2004, vol. 128, no. 4, pp. 9-12 (Russian). 3. Pilidi V. S. O metode sglazhivanija kojefficientov dlja singuljarnyh integral'nyh operatorov. Sovremennye Metody i Problemy Teorii Operatorov i Garmonicheskogo Analiza i ih Prilozhenija-IV. Tezisy Dokladov [Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis IV], Rostov n/D., ZAO "Centr universal'noj poligrafii", 2014, p. 38 (Russian). 4. Pilidi V. S. Criteria for uniform invertibility of regular approximations of one-dimensional singular integral operators with piecewise continuous coefficients. Math. of the USSR-Izvestiya, 1991, vol. 37, no. 3, pp. 631-655. 5. Gohberg I. C., Krupnik N. Ja. Vvedenie v Teoriju Odnomernyh Singuljarnyh Integral'nyh Operatorov, Kishinev, "Shtiinca", 1973, 426 p. (Russian). ← Contents of issue


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