{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,16]],"date-time":"2025-05-16T10:43:51Z","timestamp":1747392231828},"publisher-location":"Basel","reference-count":38,"publisher":"Birkh\u00e4user Basel","isbn-type":[{"type":"print","value":"9783034894715"},{"type":"electronic","value":"9783034881999"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2002]]},"DOI":"10.1007\/978-3-0348-8199-9_8","type":"book-chapter","created":{"date-parts":[[2011,8,4]],"date-time":"2011-08-04T03:16:54Z","timestamp":1312427814000},"page":"107-144","source":"Crossref","is-referenced-by-count":3,"title":["Singular Integral Equations on Piecewise Smooth Curves in Spaces of Smooth Functions"],"prefix":"10.1007","author":[{"given":"L. P.","family":"Castro","sequence":"first","affiliation":[]},{"given":"R.","family":"Duduchava","sequence":"additional","affiliation":[]},{"given":"F.-O.","family":"Speck","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"8_CR1","volume-title":"Operator Theory: Advances and Applications","author":"R Akhmerov","year":"1992","unstructured":"R. Akhmerov, M. Kamenskij, A. Potapov, R. Rodkina and B. Sadovskij, Measures of Noncompactness and Condensing Operators (Transl. from the Russian), Operator Theory: Advances and Applications 55, Birkh\u00e4user, Basel 1992."},{"key":"8_CR2","volume-title":"Progress in Mathematics","author":"A B\u00f6ttcher","year":"1997","unstructured":"A. B\u00f6ttcher and Yu.I. Karlovich, Carleson Curves, Muckenhoupt Weights, and Toeplitz Operators, Progress in Mathematics 154, Birkh\u00e4user Verlag, Basel 1997."},{"key":"8_CR3","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1002\/1522-2616(200102)222:1<79::AID-MANA79>3.0.CO;2-3","volume":"222","author":"O Chkadua","year":"2001","unstructured":"O. Chkadua and R. Duduchava, Pseudodifferential equations on manifolds with boundary: Fredholm property and asymptotic, Mathematische Nachrichten 222 (2001), 79\u2013139.","journal-title":"Mathematische Nachrichten"},{"key":"8_CR4","first-page":"304","volume":"11","author":"R Duduchava","year":"1970","unstructured":"R. Duduchava, On singular integral operators in Holder spaces with weights, Sov. Math. Dokl 11 (1970), 304\u2013308; translation from Dokl. Akad. Nauk SSSR 191 (1970), 16-19.","journal-title":"Sov. Math. Dokl"},{"issue":"1","key":"8_CR5","first-page":"56","volume":"5","author":"R Duduchava","year":"1970","unstructured":"R. Duduchava, On the boundedness of the singular integral operator in H\u00f6lder spaces with weights, Matematicheskie Issledovania 5:1 (1970), 56\u201376, Kishinev, Stiintsa (Russian).","journal-title":"Matematicheskie Issledovania"},{"key":"8_CR6","first-page":"19","volume":"41","author":"R Duduchava","year":"1973","unstructured":"R. Duduchava, The algebra of one-dimensional singular integral operators in spaces of H\u00f6lder functions with weight, Trudy Tbiliskogo Matematicheskogo In-stituta Akademii Nauk Gruzinskoi SSR 41 (1973), 19\u201352 (Russian).","journal-title":"Trudy Tbiliskogo Matematicheskogo In-stituta Akademii Nauk Gruzinskoi SSR"},{"key":"8_CR7","first-page":"109","volume-title":"Research Notes in Mathematics","author":"R Duduchava","year":"1976","unstructured":"R. Duduchava, On singular integral operators on piecewise smooth lines; in: Research Notes in Mathematics 8, Functional Theoretic Methods in Differential Equations, Pitman, London, pp. 109\u2013131, 1976."},{"key":"8_CR8","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1070\/SM1976v030n04ABEH002286","volume":"30","author":"R. Duduchava","year":"1976","unstructured":"R. Duduchava, On bisingular integral operators with discontinuous coefficients, Mathematics USSR, Sbornik 30 (1976), 515\u2013537.","journal-title":"Mathematics USSR, Sbornik"},{"key":"8_CR9","volume-title":"Integral Equations with Fixed Singularities","author":"R Duduchava","year":"1979","unstructured":"R. Duduchava, Integral Equations with Fixed Singularities, Teubner, Leipzig 1979."},{"key":"8_CR10","first-page":"15","volume":"42","author":"R. Duduchava","year":"1984","unstructured":"R. Duduchava, On general singular integral operators of the plane theory of elasticity, Rendiconti Sem. Mat. Univers. e Politecn. Torino 42: 3 (1984), 15\u201341.","journal-title":"Rendiconti Sem. Mat. Univers. e Politecn. Torino"},{"key":"8_CR11","first-page":"41","volume":"11","author":"R Duduchava","year":"1984","unstructured":"R. Duduchava, On multidimensional singular integral operators, I-II, Journal of Operator Theory 11 (1984), 41\u201376, 199-214.","journal-title":"Journal of Operator Theory"},{"key":"8_CR12","doi-asserted-by":"publisher","first-page":"505","DOI":"10.1007\/BF01201150","volume":"10","author":"R Duduchava","year":"1987","unstructured":"R. Duduchava, On algebras generated by convolutions and discontinuous functions, Integral Equations and Operator Theory 10 (1987), 505\u2013530.","journal-title":"Integral Equations and Operator Theory"},{"key":"8_CR13","first-page":"40","volume":"76","author":"R Duduchava","year":"1985","unstructured":"R. Duduchava and T. Latsabidze, On the index of singular integral equations with complex conjugate functions on piecewise smooth lines, Trudy Tbilisskogo Matematicheskogo Instituta Akademii Nauk Gruzinskoi SSR 76 (1985), 40\u201359 (Russian).","journal-title":"Trudy Tbilisskogo Matematicheskogo Instituta Akademii Nauk Gruzinskoi SSR"},{"key":"8_CR14","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF01195488","volume":"22","author":"R Duduchava","year":"1995","unstructured":"R. Duduchava, T. Latsabidze and A. Saginashvili, Singular integral operators with the complex conjugation on curves with cusps, Integral Equations and Operator Theory 22 (1995), 1\u201336.","journal-title":"Integral Equations and Operator Theory"},{"key":"8_CR15","first-page":"1","volume":"21","author":"R Duduchava","year":"2000","unstructured":"R. Duduchava and B. Silbermann, Boundary value problems in domains with peaks, Memoirs on Differential Equations and Mathematical Physics 21 (2000), 1\u2013121.","journal-title":"Memoirs on Differential Equations and Mathematical Physics"},{"key":"8_CR16","unstructured":"R. Duduchava and B. Silbermann, The Cisotti formulae and conformal mapping of domains with peaks (to appear)."},{"key":"8_CR17","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1002\/mana.3211600107","volume":"160","author":"R Duduchava","year":"1993","unstructured":"R. Duduchava and F.-O. Speck, Pseudo-differential operators on compact manifolds with Lipschitz boundary, Mathematische Nachrichten 160 (1993), 149\u2013191.","journal-title":"Mathematische Nachrichten"},{"key":"8_CR18","doi-asserted-by":"crossref","first-page":"633","DOI":"10.1515\/GMJ.2000.633","volume":"7","author":"R Duduchava","year":"2000","unstructured":"R. Duduchava and F.-O. Speck, Singular integral equations in special weighted spaces, Georgian Mathematical Journal 7 (2000), 633\u2013642.","journal-title":"Georgian Mathematical Journal"},{"key":"8_CR19","doi-asserted-by":"publisher","first-page":"271","DOI":"10.1002\/mana.19901461703","volume":"146","author":"J Elschner","year":"1990","unstructured":"J. Elschner, On spline approximation for a class of non-compact integral equations, Mathematische Nachrichten 146 (1990), 271\u2013321.","journal-title":"Mathematische Nachrichten"},{"key":"8_CR20","volume-title":"Boundary Value Problems for Elliptic Pseudodifferential Equations","author":"G Eskin","year":"1981","unstructured":"G. Eskin, Boundary Value Problems for Elliptic Pseudodifferential Equations AMS, Providence, Rhode Island 1981."},{"key":"8_CR21","volume-title":"Operator Theory: Advances and Applications","author":"I Gohberg","year":"1992","unstructured":"I. Gohberg and N. Krupnik, One-Dimensional Linear Singular Integral Equations, I-II, Operator Theory: Advances and Applications 53-54, Birkh\u00e4user Verlag, Basel 1992."},{"key":"8_CR22","first-page":"3","volume":"23","author":"B Khvedelidze","year":"1957","unstructured":"B. Khvedelidze, Linear discontinuous boundary value problems of function theory, singular integral equations and their applications, Trudy Tbilisskogo Matematich-eskogo Instituta Akademii Nauk Gruzinskoi SSR 23 (1957), 3\u2013158 (Russian).","journal-title":"Trudy Tbilisskogo Matematich-eskogo Instituta Akademii Nauk Gruzinskoi SSR"},{"key":"8_CR23","first-page":"229","volume":"1","author":"M Krasnosel\u2019skij","year":"1960","unstructured":"M. Krasnosel\u2019skij, On a theorem of M. Riesz, Sov. Math. Dokl 1 (1960), 229\u2013231; translation from Dokl. Akad. Nauk SSSR 131 (1960), 246-248.","journal-title":"Sov. Math. Dokl"},{"key":"8_CR24","doi-asserted-by":"crossref","unstructured":"G. Litvinchuk, Solvability Theory of Boundary Value Problems and Singular In tegral Equations With Shift, Mathematics and its Applications 523, Kluwer Academic Publishers, Dordrecht 2000.","DOI":"10.1007\/978-94-011-4363-9"},{"key":"8_CR25","volume-title":"Monographs and Studies in Mathematics","author":"V Mazya","year":"1985","unstructured":"V. Maz\u2019ya and T. Shaposhnikova, Theory of Multipliers in Spaces of Differentiate Functions, Monographs and Studies in Mathematics 23, Pitman, Boston 1985."},{"key":"8_CR26","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1007\/BF01193508","volume":"32","author":"V Mazya","year":"1998","unstructured":"V. Maz\u2019ya and A. Solov\u2019ev, L p -theory of boundary integral equations on a contour with outward peak, Integral Equations and Operator Theory 32 (1998), 75\u2013100.","journal-title":"Integral Equations and Operator Theory"},{"key":"8_CR27","volume-title":"Singular Integral Equations","author":"N Muskhelishvili","year":"1953","unstructured":"N. Muskhelishvili, Singular Integral Equations, Nordhoff, Groningen 1953 (The last Russian edition: Nauka, Moscow 1968)."},{"key":"8_CR28","volume-title":"Mathematical Topics","author":"B Paneah","year":"2000","unstructured":"B. Paneah, The Oblique Derivative Problem. The Poincar\u00e9-problem, Mathematical Topics 17, Wiley-VCH, Weinheim 2000."},{"key":"8_CR29","volume-title":"Randeigenschaften analytischer Funktionen","author":"I Privalov","year":"1956","unstructured":"I. Privalov, Randeigenschaften analytischer Funktionen, Deutscher Verlag der Wissenschaften, Berlin 1956 (Russian original: GITTL, Moskva 1950)."},{"key":"8_CR30","first-page":"107","volume-title":"Semin. Anal.","author":"R P\u00f6ltz","year":"1986","unstructured":"R. P\u00f6ltz, Operators of local type in spaces of H\u00f6lder functions, Semin. Anal. 1986\/87, Weierstrass Institute, Berlin 1987, 107\u2013122 (Russian)."},{"key":"8_CR31","volume-title":"Operator Theory: Advances and Applications","author":"S Pr\u00f6\u00dfdorf","year":"1991","unstructured":"S. Pr\u00f6\u00dfdorf and B. Silbermann, Numerical Analysis for Integral and Related Operator Equations, Operator Theory: Advances and Applications 52, Birkh\u00e4user Verlag, Basel 1991."},{"key":"8_CR32","first-page":"452","volume":"12","author":"V Rabinovich","year":"1971","unstructured":"V. Rabinovich, Pseudodifferential equations in unbounded regions, Sov. Math. Dokl. 12 (1971), 452\u2013456 (translation from Dokl. Akad. Nauk SSSR 197 (1971), 284-287.","journal-title":"Sov. Math. Dokl."},{"key":"8_CR33","doi-asserted-by":"publisher","first-page":"854","DOI":"10.1007\/BF01196881","volume":"12","author":"S Roch","year":"1989","unstructured":"S. Roch and B. Silbermann, The Calkin image of algebras of singular integral operators, Integral Equations and Operator Theory 12 (1989), 854\u2013897.","journal-title":"Integral Equations and Operator Theory"},{"issue":"1","key":"8_CR34","first-page":"37","volume":"33","author":"H Schulze","year":"1991","unstructured":"H. Schulze, On singular integral operators on weighted Holder spaces, Wiss. Z. Techn. Univ. Chemnitz 33:1 (1991), 37\u201347.","journal-title":"Wiss. Z. Techn. Univ. Chemnitz"},{"key":"8_CR35","first-page":"567","volume":"29","author":"I Simonenko","year":"1965","unstructured":"I. Simonenko, A new general method of investigating linear operator equations of the type of singular integral equations, I, II Izv. Akad. Nauk SSSR, Ser. Mat. 29 (1965), 567\u2013586, 757-782 (Russian).","journal-title":"Izv. Akad. Nauk SSSR, Ser. Mat."},{"key":"8_CR36","unstructured":"F.-O. Speck, On Generalized Convolution Operators and a Class of Integro-Differential Equations, PhD dissertation, TH Darmstadt, 1974 (German)."},{"key":"8_CR37","volume-title":"Singular Integrals and Differentiability Properties of Functions","author":"E Stein","year":"1970","unstructured":"E. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton 1970."},{"key":"8_CR38","volume-title":"Interpolation Theory, Function Spaces, Differential Operators","author":"H Triebel","year":"1995","unstructured":"H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, 2nd edition, Johann Ambrosius Barth Verlag, Heidelberg and Leipzig 1995.","edition":"2"}],"container-title":["Toeplitz Matrices and Singular Integral Equations"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-0348-8199-9_8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,13]],"date-time":"2019-06-13T19:13:32Z","timestamp":1560453212000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-0348-8199-9_8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002]]},"ISBN":["9783034894715","9783034881999"],"references-count":38,"URL":"https:\/\/doi.org\/10.1007\/978-3-0348-8199-9_8","relation":{},"subject":[],"published":{"date-parts":[[2002]]}}}