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Convolution integral equations with discontinuous presymbols, singular integral equations with fixed singularities, and their applications to problems in mechanics. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze 60 (1979), 136 pp.
Integral equations in convolution with discontinuous presymbols, singular integral equations with fixed singularities, and their applications to some problems of mechanics. BSB B. G. Teubner Verlagsgesellschaft, Leipzig, 1979, 172 pp.
Boundary value problems in domains with peaks (with B. Silbermann). Mem. Differential Equations Math. Phys. 21 (2000), 1-122.
(ii) ÓÀÌÄÝÍÉÄÒÏ ÓÔÀÔÉÄÁÉ
Singular integral operators in a Hölder space with weight. (Russian) Dokl. Akad. Nauk SSSR 191 (1970), 16-19; English transl.: Sov. Math., Dokl. 11 (1970), 304-308.
The boundedness of the singular integration operator in Hölder spaces with weight. (Russian) Mat. Issled. 5 (1970), No. 1(15), 56-76.
Singular integral equations in Hölder spaces with weight, I. Hölder coefficients. (Russian) Mat. Issled. 5 (1970), No. 2(16), 104-124.
Singular integral equations in Hölder spaces with weight, II. Partial Hölder coefficients. (Russian) Mat. Issled. 5 (1970), No. 3(17), 58-82.
The boundary value problem for systems of discrete Wiener-Hopf equations. (Russian) Mat. Issled. 7 (1972), No. 2(24), 234-240
Discrete Wiener-Hopf equations that are composed of the Fourier coefficients of piecewise Wiener functions. (Russian) Dokl. Akad. Nauk SSSR 207 (1972), 1273-1276; English transl.: Sov. Math., Dokl. 13 (1972), 1903-1907.
The algebras of singular integral operators in spaces of Hölder functions with weight. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 65 (1972), 25-28.
Discrete Wiener-Hopf equations in spaces with weight. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 67 (1972), 17-20.
Wiener-Hopf integral operators with discontinuous symbols. (Russian) Dokl. Akad. Nauk SSSR 211 (1973), 277-280; English transl.: Sov. Math., Dokl. 14 (1973), 1001-1005.
Algebras of one-dimensional singular integral operators in space of Hölder functions with weight. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze 43 (1973), 19-52.
Noether theorems for singular integral equations in spaces of Hölder functions with weight. (Russian) Proceedings of the Symposium on Continuum Mechanics and Related Problems of Analysis (Tbilisi, 1971), Vol. 1 (Russian), pp. 89-102. “Mecniereba”, Tbilisi, 1973.
Singular integral operators on piecewise smooth curves. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 71 (1973), 553-556.
Multidimensional convolution equations formed from the Fourier coefficients of discontinuous functions. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 74 (1974), 277-280.
Discrete convolution operators on symmetric spaces of sequences with weights. Tresses of the Conference of Young Scientists and Postgraduates, Tbilisi State University, I. Vekua Institute of Applied Mathematics, 63-64, Tbilisi University Press, Tbilisi, 1974.
Singular integral equations with unbounded coefficients. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze 44 (1974), 72-78.
Convolution integral operators with discontinuous coefficients. (Russian) Dokl. Akad. Nauk SSSR 218 (1974), 264-267; English transl.: Sov. Math., Dokl. 15 (1974), 1302-1306.
Bisingular integral operators and convolution operators in a quadrant. (Russian) Dokl. Akad. Nauk SSSR 221 (1975), No. 2, 279-282; English transl.: Sov. Math., Dokl. 16 (1975), 330-334.
Wiener-Hopf integral operators. (Russian) Math. Nachr. 65 (1975), 59-82.
Convolution integral operators with discontinuous symbols. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze 50 (1975), 34-41.
The discrete Wiener-Hopf equations. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze 50 (1975), 42-59.
Bisingular integral operators, and boundary value problems of the theory of analytic functions in spaces of generalized functions. (Russian) Dokl. Akad. Nauk SSSR 224 (1975), No. 5, 996-999; English transl.: Sov. Math., Dokl. 16 (1975), 1324-1328.
Integral convolution operators on the quadrant with discontinuous symbols. (Russian) Izv. Akad. Nauk SSSR Ser. Mat. 40 (1976), No. 2, 388-412; English transl.: Izv. Math. USSR 10 (1976), 371-392.
Bisingular integral operators with discontinuous coefficients. (Russian) Mat. Sb. (N.S.) 101(143) (1976), No. 4, 584-609; English transl.: Sb. Math. USSR 30 (1976), 515-537.
On singular integral operators on piecewise smooth lines. Function theoretic methods in differential equations, pp. 109-131. Res. Notes in Math., No. 8, Pitman, London, 1976.
A uniqueness theorem for the integral equation of a thin rectangular airfoil (with V. G. Maz’ja). (Russian) Soobshch. Akad. Nauk Gruzin. SSR 87 (1977), No. 1, 53-56.
Integral operators of convolution type with discontinuous coefficients. (Russian) Math. Nachr. 79 (1977), 75-98.
Discrete convolution operators on the quarter plane, and their indices. (Russian) Izv. Akad. Nauk SSSR Ser. Mat. 41 (1977), No. 5, 1125-1137; English transl.: Izv. Math. USSR 11 (1977), 1072-1084.
Singular integral equations with fixed singularities in the kernel on piecewise smooth lines. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 91 (1978), No. 2, 293-296.
Some integral equations with singular kernels. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 92 (1978), No. 1, 21-24.
Integral equations of convolution type with discontinuous coefficients. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 92 (1978), No. 2, 281-284.
On the index of bisingular integral operators, I. (Russian) Math. Nachr. 91 (1979), 431-460.
On the index of bisingular integral operators, II. (Russian) Math. Nachr. 92 (1979), 289-307.
Integral equation of convolution type (with B. Khvedelidze). Mathematical Encyclopaedia v. 2, Sovetskaya Entsiklopedia, Moscow, 1979.
Solution of a convolution equation on a quadrant. (Russian) Mat. Zametki 27 (1980), No. 3, 415-427; English transl.: Math. Notes 27 (1980), 207-213.
Integral convolution operators on the half axis with semi-almost-periodic presymbols (with A. I. Saginashvili). (Russian) Soobshch. Akad. Nauk Gruzin. SSR 98 (1980), No. 1, 21-24.
Integral equations of convolution on the half axis with semi-almost-periodic presymbols (with A. I. Saginashvili). (Russian) Differentsial’nye Uravneniya 17 (1981), No. 2, 301-312, 389-390; English transl.: Differ. Equations 17 (1981), 207-216.
An application of singular integral equations to some problems of elasticity. Integral Equations Operator Theory 5 (1982), No. 4, 475-489.
Multidimensional singular integral equations. Preliminary theorems. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 109 (1983), No. 2, 241-244.
Multidimensional singular integral equations. Fundamental theorems. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 111 (1983), No. 3, 465-468.
The index of singular integral equations with complex-conjugate functions on piecewise smooth lines (with T. I. Latsabidze). (Russian) Soobshch. Akad. Nauk Gruzin. SSR 115 (1984), No. 1, 29-32.
On multidimensional singular integral operators, I. The half-space case. J. Operator Theory 11 (1984), No. 1, 41-76.
On multidimensional singular integral operators, II. The case of compact manifolds. J. Operator Theory 11 (1984), No. 2, 199-214.
On general singular integral operators of the plane theory of elasticity. Rend. Sem. Mat. Univ. Politec. Torino 42 (1984), No. 3, 15-41.
The Riemann-Hilbert boundary value problem in a bicylinder (with L. Rodino). Boll. Un. Mat. Ital. A (6) 4 (1985), No. 2, 327-336.
The index of singular integral equations with complex-conjugate functions on piecewise-smooth lines (with T. I. Latsabidze). (Russian) Trudy Tbiliss. Mat. Inst. Razmadze 76 (1985), 40-59.
General singular integral equations and fundamental problems of the plane theory of elasticity. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze 82 (1986), 45-89.
On algebras generated by convolutions and discontinuous functions. Special issue: Wiener-Hopf problems and applications (Oberwolfach, 1986). Integral Equations Operator Theory 10 (1987), No. 4, 505-530.
The algebra of nonclassical singular integral operators on half space. Special issue: Wiener-Hopf problems and applications (Oberwolfach, 1986) (with R. Schneider). Integral Equations Operator Theory 10 (1987), No. 4, 531-553.
On the regularization of the singular integral operators (with G. Mjzavia). In: Abstracts of the conference “Operator Theory, Advances and Applications”, Calgary, August, 1988.
Continuity of generalized solutions of fundamental boundary value problems in the mathematical theory of cracks (with D. G. Natroshvili and E. M. Shargorodsky). (Russian) Soobshch. Akad. Nauk Gruzin. SSR 135 (1989), No. 3, 497-500.
Basic boundary value problems of the mathematical theory of cracks for anisotropic media (with D. Natroshvili and E. Shargorodsky). (Russian) Proc. of the extended seminar of I. Vekua Inst. Appl. Math. 4 (1989), No. 2, 87-90.
Boundary value problems of the mathematical theory of cracks (with D. Natroshvili and E. Shargorodsky). Tbiliss. Gos. Univ. Inst. Prikl. Mat. Trudy 39 (1990), 68-84.
Some singular integral operators with fixed singularities (with E. M. Shargorodsky). (Russian) Trudy Tbiliss. Mat. Inst. Razmadze 93 (1990), 3-35.
Singular integral operators with complex conjugation on piecewise-smooth lines (with T. L. Latsabidze and A. I. Saginashvili). (Russian) Soobshch. Akad. Nauk Gruzii 146 (1992), No. 1, 21-24.
Bessel potential operators for the quarter-plane (with F.-O. Speck). Appl. Anal. 45 (1992), No. 1-4, 49-68.
Wiener-Hopf equations with the transmission property. Integral Equations Operator Theory 15 (1992), No. 3, 412-426.
Pseudodifferential operators on compact manifolds with Lipschitz boundary (with F.-O. Speck). Math. Nachr. 160 (1993), 149-191.
On the norm of singular integral operator on curves with cusps (with N. Krupnik). Integral Equations Operator Theory 20 (1994), No. 4, 377-382.
Basic boundary value problems of thermoelasticity for anisotropic bodies with cuts, I (with D. Natroshvili and E. Shargorodsky). Georgian Math. J. 2 (1995), No. 2, 123-140.
Basic boundary value problems of thermoelasticity for anisotropic bodies with cuts, II (with D. Natroshvili and E. Shargorodsky). Georgian Math. J. 2 (1995), No. 3, 259-276.
Two-dimensional singular integral operators with shift (with A. I. Saginashvili and E. M. Shargorodsky). (Russian) Trudy Tbiliss. Mat. Inst. Razmadze 103 (1995), 3-13.
On the approximation of singular integral equations by equations with smooth kernels (with S. Prössdorf). Integral Equations Operator Theory 21 (1995), No. 2, 224-237.
Singular integral operators with the complex conjugation on curves with cusps (with T. Latsabidze and A. Saginashvili). Integral Equations Operator Theory 22 (1995), No. 1, 1-36.
Finite interval convolution operators on the Bessel potential spaces (with M. A. Bastos and A. F. dos Santos). Math. Nachr. 173 (1995), 49-63.
The Wiener-Hopf method for systems of pseudodifferential equations with an application to crack problems (with W. L. Wendland). Integral Equations Operator Theory 23 (1995), No. 3, 294-335.
The Wiener-Hopf method in crack and interface problems (with A.-M. Sändig and W. L. Wendland). Z. Angew. Math. Mech. 76 (1996), No. 2, 113-116.
On two-dimensional singular integral operators with conformal Carleman shift (with A. Saginashvili and E. Shargorodsky). J. Operator Theory 37 (1997), No. 2, 263-279.
Bessel potential operator. Encyclopaedia of Mathematics, Supplement Volume I, 116-117, Ed. Prof. M. Hazewinkel, Kluwer Acad. Publ., 1997.
Mixed crack type problem in anisotropic elasticity (with D. Natroshvili). Math. Nachr. 191 (1998), 83-107.
Asymptotics of solutions to some boundary value problems of elasticity for bodies with cuspidal edges (with O. Chkadua). Mem. Differential Equations Math. Phys. 15 (1998), 29-58.
Asymptotics of solutions to a pseudodifferential equations (with O. Chkadua). Bull. Georgian Acad. Sci. 158 (1998), No. 2, 207-210.
Asymptotics of potential-type functions (with O. Chkadua). Bull. Georgian Acad. Sci. 159 (1999), No. 1, 23-27.
Asymptotics of solutions to the crack problem (with R. O. Chkadua). Bull. Georgian Acad. Sci. 159 (1999), No. 3, 389-391.
An algebra of integral operators with fixed singularities in kernels (with N. Krupnik and E. Shargorodsky). Integral Equations Operator Theory 33 (1999), No. 4, 406-425.
Interface cracks in anisotropic composites (with A.-M. Sändig and W. L. Wendland). Math. Methods Appl. Sci. 22 (1999), No. 16, 1413-1446.
On the Prandtl equation (with D. Kapanadze). Georgian Math. J. 6 (1999), No. 6, 525-536.
Asymptotics of functions represented by potentials (with O. Chkadua). Russ. J. Math. Phys. 7 (2000), No. 1, 15-47.
Singular integral equations in special weighted spaces (with F.-O. Speck). Georgian Math. J. 7 (2000), No. 4, 633-642.
Pseudodifferential equations on manifolds with boundary: Fredholm property and asymptotic (with O. Chkadua). Math. Nachr. 222 (2001), 79-139.
The Green formula and layer potentials. Integral Equations Operator Theory 41 (2001), No. 2, 127-178.
Singular integral equations on piecewise smooth curves in spaces of smooth functions (with L. P. Castro and F.-O. Speck). Toeplitz matrices and singular integral equations (Pobershau, 2001), 107-144, Oper. Theory Adv. Appl., 135, Birkhäuser, Basel, 2002.
Asymptotics without logarithmic terms for crack problems (with M. Costabel, M. Dauge). Comm. Partial Differential Equations (to appear).
The spline collocation method for Mellin convolution equations (with D. Elliott and W. L. Wendland). Universität Stuttgart, Sonderforschungsbereich 404, Bericht 96/04, 1-20, 1996.
Cracks on the interface of anisotropic composite bodies. Asymptotics of solutions (with A. M. Sändig and W. L. Wendland). Universität Stuttgart, Preprint 95-9, 1-71, 1995.
Mapping properties of the Boltzmann collision operator (with S. Rjasanow). Universität des Saarlandes, achrichtung 6.1 – Mathematik, Preprint 32, 1-30, Saarbrücken, 2001 (to appear).
Boundary value problems on a smooth surface with the smooth boundary. Universität Stuttgart, Preprint 2002-5, 1-19, 2002.
Pseudodifferential operators with applications to some problems of mathematical physics. (Lectures at Stuttgart University, Full semester 2001-2002). Universität Stuttgart, Preprint 2002-6, 1-176, 2002.
Asymptotic of potentials in the edge calculus (with D. Kapanadze and B. W. Schulze). Preprint University of Potsdam, 2003.
Crack-type boundary value problems of electroelasticity (with T. Buchukuri and O. Chkadua). Integral Equations Operator Theory 47 (2003), No. 4, 417-441.