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Izv. Akad. Nauk SSSR Ser. Mat., 1965, Volume 29, Issue 3, Pages 567–586 (Mi izv2921)  

This article is cited in 36 scientific papers (total in 36 papers)

A new general method of investigating linear operator equations of singular integral equation type. I

I. B. Simonenko


Full text: PDF file (1883 kB)

Bibliographic databases:
UDC: 517.9
Received: 28.03.1964

Citation: I. B. Simonenko, “A new general method of investigating linear operator equations of singular integral equation type. I”, Izv. Akad. Nauk SSSR Ser. Mat., 29:3 (1965), 567–586

Citation in format AMSBIB
\Bibitem{Sim65}
\by I.~B.~Simonenko
\paper A~new general method of investigating linear operator equations of singular integral equation type.~I
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1965
\vol 29
\issue 3
\pages 567--586
\mathnet{http://mi.mathnet.ru/izv2921}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=179630}
\zmath{https://zbmath.org/?q=an:0146.13101}


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    This publication is cited in the following articles:
    1. I. B. Simonenko, “Some general questions in the theory of the Riemann boundary problem”, Math. USSR-Izv., 2:5 (1968), 1091–1099  mathnet  crossref  mathscinet  zmath
    2. V. S. Rabinovich, “Pseudodifferential equations in unbounded regions with conical structure at infinity”, Math. USSR-Sb., 9:1 (1969), 73–92  mathnet  crossref  mathscinet  zmath
    3. I. B. Simonenko, “On the question of the solvability of bisingular and polysingular equations”, Funct. Anal. Appl., 5:1 (1971), 81–83  mathnet  crossref  mathscinet  zmath
    4. V. S. Rabinovich, “Pseudodifferential operators on a class of noncompact manifolds”, Math. USSR-Sb., 18:1 (1972), 45–59  mathnet  crossref  mathscinet  zmath
    5. V. S. Rabinovich, “A priori estimates and the Fredholm property for a class of pseudodifferential operators”, Math. USSR-Sb., 21:2 (1973), 191–206  mathnet  crossref  mathscinet  zmath
    6. R. V. Duduchava, “On bisingular integral operators with discontinuous coefficients”, Math. USSR-Sb., 30:4 (1976), 515–537  mathnet  crossref  mathscinet  zmath  isi
    7. R. V. Duduchava, “Convolution integral operators on a quadrant with discontinuous symbols”, Math. USSR-Izv., 10:2 (1976), 371–392  mathnet  crossref  mathscinet  zmath
    8. I. M. Spitkovsky, “Some estimates for the partial indices of measurable matrix-valued functions”, Math. USSR-Sb., 39:2 (1981), 207–226  mathnet  crossref  mathscinet  zmath  isi
    9. B. J. Steinberg, “Convolution operators on locally compact groups”, Funct. Anal. Appl., 15:3 (1981), 233–234  mathnet  crossref  mathscinet  zmath  isi
    10. Yu. I. Karlovich, V. G. Kravchenko, “An algebra of singular integral operators with piecewise-continuous coefficients and a piecewise-smooth shift on a composite contour”, Math. USSR-Izv., 23:2 (1984), 307–352  mathnet  crossref  mathscinet  zmath
    11. N. L. Vasilevskii, “Algebras generated by multidimensional singular integral operators and by coefficients admitting discontinuities of homogeneous type”, Math. USSR-Sb., 57:1 (1987), 1–19  mathnet  crossref  mathscinet  zmath
    12. N. Ya. Krupnik, “Exact constant in Simonenko's theorem on an envelope of a family of operators of local type”, Funct. Anal. Appl., 20:2 (1986), 144–145  mathnet  crossref  mathscinet  zmath  isi
    13. N. L. Vasilevskii, “On an algebra connected with Toeplitz operators in radial tube domains”, Math. USSR-Izv., 30:1 (1988), 71–88  mathnet  crossref  mathscinet  zmath
    14. R. E. Avedan'o, N. Ya. Krupnik, “Local principle of computation of the factor-norms of singular integral operators”, Funct. Anal. Appl., 22:2 (1988), 130–131  mathnet  crossref  mathscinet  zmath  isi
    15. Karlovich I., “On Algebras of Singular Integral-Operators with Discrete-Groups of Shifts in Lp Spaces”, 304, no. 2, 1989, 274–280  isi
    16. V. S. Pilidi, “Criteria for uniform invertibility of regular approximations of one-dimensional singular integral operators with piecewise continuous coefficients”, Math. USSR-Izv., 37:3 (1991), 631–655  mathnet  crossref  mathscinet  zmath  adsnasa
    17. V. M. Deundyak, I. B. Simonenko, V. A. Stukopin, “Ideals of a Banach Algebra of Singular Integral Operators with Piecewise Continuous Coefficients in the Space $L_p$”, Funct. Anal. Appl., 27:4 (1993), 277–279  mathnet  crossref  mathscinet  zmath  isi
    18. V. V. Kisil, “Local behavior of two-sided convolution operators with singular kernels on the Heisenberg group”, Math. Notes, 56:2 (1994), 790–800  mathnet  crossref  mathscinet  zmath  isi
    19. V. V. Kisil, “Local algebras of two-sided convolutions on the Heisenberg group”, Math. Notes, 59:3 (1996), 261–268  mathnet  crossref  crossref  mathscinet  zmath  isi
    20. L. I. Sazonov, “$C^*$-algebras of bisingular operators with discontinuous coefficients”, Izv. Math., 63:2 (1999), 367–399  mathnet  crossref  crossref  mathscinet  zmath  isi
    21. O. G. Avsyankin, N. K. Karapetyants, “On the algebra of multidimensional integral operators with homogeneous kernels with variable coefficients”, Russian Math. (Iz. VUZ), 45:1 (2001), 1–8  mathnet  mathscinet  zmath  elib
    22. E. A. Maksimenko, “Convolution operators on expanding polyhedra: limits of the norms of inverse operators and pseudospectra”, Siberian Math. J., 44:6 (2003), 1027–1038  mathnet  crossref  mathscinet  zmath  isi  elib
    23. L. I. Sazonov, “Two-Dimensional Töplitz Operators with Measurable Symbols”, Math. Notes, 74:1 (2003), 81–90  mathnet  crossref  crossref  mathscinet  zmath  isi
    24. Galina Vornicescu, “On regularization of singular operators with Carleman shift”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2003, no. 3, 104–106  mathnet  mathscinet
    25. L. I. Sazonov, “On applicability of the projection method to two-dimensional Toeplitz operators with measurable symbol”, Siberian Math. J., 47:3 (2006), 526–536  mathnet  crossref  mathscinet  zmath  isi  elib
    26. V. E. Nazaikinskii, A. Yu. Savin, B. Yu. Sternin, “Noncommutative geometry and classification of elliptic operators”, Journal of Mathematical Sciences, 164:4 (2010), 603–636  mathnet  crossref  mathscinet  elib
    27. Karlovich A.Yu., “Singular Integral Operators on Variable Lebesgue Spaces over Arbitrary Carleson Curves”, Topics in Operator Theory: Operators, Matrices and Analytic Functions, Operator Theory Advances and Applications, 1, 2010, 321–336  isi
    28. Rabinovich V., Samko S., “Pseudodifferential Operators Approach to Singular Integral Operators in Weighted Variable Exponent Lebesgue Spaces on Carleson Curves”, Integral Equations Operator Theory, 69:3 (2011), 405–444  crossref  isi
    29. V. S. Rabinovich, S. G. Samko, “Singular Integral Operators on Weighted Variable Exponent Lebesgue Spaces on Composed Carleson Curves”, Funct. Anal. Appl., 46:1 (2012), 73–76  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    30. Evgueniya Dyachenko, Nikolai Tarkhanov, “Degeneration of Boundary Layer at Singular Points”, Zhurn. SFU. Ser. Matem. i fiz., 6:3 (2013), 283–297  mathnet
    31. V. S. Rabinovich, “Acoustic Diffraction Problems on Periodic Graphs”, Funct. Anal. Appl., 48:4 (2014), 298–303  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    32. A. V. Lukin, “Primenenie lokalnogo podkhoda Simonenko–Kozaka v teorii proektsionnykh metodov resheniya uravnenii svertki s operatornymi koeffitsientami”, Vladikavk. matem. zhurn., 18:2 (2016), 55–66  mathnet
    33. V. B. Vasilev, “Potentsialy dlya ellipticheskikh kraevykh zadach v konusakh”, Sib. elektron. matem. izv., 13 (2016), 1129–1149  mathnet  crossref
    34. Kokilashvili V. Meskhi A. Rafeiro H. Samko S., “Integral Operators in Non-Standard Function Spaces, Vol 1: Variable Exponent Lebesgue and Amalgam Spaces”, Integral Operators in Non-Standard Function Spaces, Vol 1: Variable Exponent Lebesgue and Amalgam Spaces, Operator Theory Advances and Applications, 248, Springer Int Publishing Ag, 2016, 1–567  crossref  isi
    35. A. I. Parfenov, “Series in a Lipschitz perturbation of the boundary for solving the Dirichlet problem”, Siberian Adv. Math., 27:4 (2017), 274–304  mathnet  crossref  crossref  elib
    36. A. V. Abramyan, V. S. Pilidi, “Kriterii ravnomernoi obratimosti regulyarnykh approksimatsii odnomernykh singulyarnykh integralnykh operatorov na kusochno-lyapunovskom konture”, Vladikavk. matem. zhurn., 21:1 (2019), 5–15  mathnet  crossref
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