Artigo Revisado por pares

On Fredholm Properties of a Class of Hankel Operators

2000; Wiley; Volume: 217; Issue: 1 Linguagem: Inglês

10.1002/1522-2616(200009)217

ISSN

1522-2616

Autores

Nikolai Karapetiants, Stefan Samko,

Tópico(s)

Numerical methods in inverse problems

Resumo

Mathematische NachrichtenVolume 217, Issue 1 p. 75-103 Original Paper On Fredholm Properties of a Class of Hankel Operators N.K. Karapetiants, N.K. Karapetiants [email protected] Rostov State University, Math. Department, ul. Zorge, 5, Rostov – na – DonuSearch for more papers by this authorS.G. Samko, S.G. Samko [email protected] Universidade do Algarve, Unidade de Ciencias Exactas e Humanas, Campus de Gambelas, Faro, 8000, PortugalSearch for more papers by this author N.K. Karapetiants, N.K. Karapetiants [email protected] Rostov State University, Math. Department, ul. Zorge, 5, Rostov – na – DonuSearch for more papers by this authorS.G. Samko, S.G. Samko [email protected] Universidade do Algarve, Unidade de Ciencias Exactas e Humanas, Campus de Gambelas, Faro, 8000, PortugalSearch for more papers by this author First published: 18 August 2000 https://doi.org/10.1002/1522-2616(200009)217:1 3.0.CO;2-JCitations: 5AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat References [1] Costabel, M.: A Contribution to the Theory of Singular Integral Equations with Carleman Shift, Integr. Equat. and Oper. Theory 2 (1979), 11–24 10.1007/BF01729358 Google Scholar [2] Gohberg, I., and Krupnik, N.: On Spectrum of Singular Operators in Lp, Stud. Math. 31, (4) (1968), 347–362 (Russian) Google Scholar [3] Gohberg, I., and Krupnik, N.: Singular Integral Operators with Piecewise Continuous Coefficients and Their Symbols, Izv. Akad. Nauk SSSR, ser. Mat., 35 (4) (1971), 940–964 (Russian). Transl. in Math. USSR, Izvestija 5 (1972), 955–979 Google Scholar [4] Gohberg, I., and Krupnik, N.: On One Dimensional Singular Integral Operators with Shift, Izv. Akad. Nauk Armyan. SSR, Matematika 8, (1) (1973), 3–12 (Russian) Google Scholar [5] Gohberg, I., and Krupnik, N.: One – Dimensional Linear Singular Integral Equations, Vol. I. Introduction, Operator Theory: Advances and Applications 53, Birkhäuser Verlag, Basel– Boston, 1992 Google Scholar [6] Gohberg, I., and Krupnik, N.: One – Dimensional Linear Singular Integral Equations, Vol. II. General Theory and Applications, Operator Theory: Advances and Applications 54, Birkhäuser Verlag, Basel– Boston, 1992 Google Scholar [7] Gradshtein, I.S., and Ryzhik, I.M.: Tables of Integrals, Sums, Series and Products, Fifth Edition, Academic Press, Inc., 1994 Google Scholar [8] Karapetyants, N.K., and Samko, S.G.: A Certain Class of Convolution Type Integral Equations and Its Application, Izv. Akad. Nauk SSSR, ser. Mat., 35, (3) (1971), 714–726 (Russian). Transl. in Math. USSR, Izvestija 5, No. 3 (1971), 731–744 Google Scholar [9] Karapetyants, N.K., and Samko, S.G.: Singular Integral Operators on the Axis with a Fractional – Linear Shift of Carlemanian Type the Noether Property for Operators Containing an Involution, Izv. Akad. Nauk Armyan. SSR, Matematika 7, (1) (1972), 68–77 (Russian) Google Scholar [10] Karapetyants, N.K., and Samko, S.G.: Singular Integral Equations with Carleman Shift in the Case of Discontinuous Coefficients, and a Study of whether a Certain Class of Linear Operators with Involution is Noetherian, Dokl. Akad. Nauk SSSR 211, (2) (1973), 281–284 (Russian). Transl. in Soviet Math. Dokl. 14, No. 4 (1973), 1006–1011 Web of Science®Google Scholar [11] Karapetyants, N.K., and Samko, S.G.: Singular Integral Operators with Carleman Shift in the Case of Piecewise Continuous Coefficients, I, Izv. Vysch, Uchebn. Zaved., Matematika, 43–45, (2), 1975 (Russian) Google Scholar [12] Karapetyants, N.K., and Samko, S.G.: Singular Integral Operators with Carleman Shift in the Case of Piecewise Continuous Coefficients, II, Izv. Vysch, Uchebn. Zaved., Matematika, 34–45 (3), 1975 (Russian) Google Scholar [13] Karapetyants, N.K., and Samko, S.G.: Investigation of Noether Nature of Linear Equations with Generalized Involutive Operators and Its Applications. In: Collection of Research Papers “Metody Teorii Funktsii i Funkts. Anal.”, pp. 14–21, Checheno – Ingushskii University, Groznyi, 1976 (Russian) Google Scholar [14] Karapetyants, N.K.. and Samko, S.G.: Investigation of Noether Nature of Linear Equations with Generalized Involutive Operators and Its Applications. In: Collection of Research Papers “Metody Teorii Funktsii i Funkts. Anal.”, pp. 14–21, Checheno – Ingushskii University, Groznyi, 1976 (Russian) Google Scholar [15] Kravchenko, V.G., Lebre, A., Litvinchuk, G.S., and Teixeira, F.: Fredholm Theory for a Class of Singular Integral Operators with Carleman Shift and Unbounded Coefficients, Math. Nachr. 172 (1995), 199–210 10.1002/mana.19951720115 Web of Science®Google Scholar [16] Lebre, A., Meister, E., and Teixeira, F.: Some Results on the Invertibility of Wiener – Hopf – Hankel Operators, Z. Anal. Angew. 11 (1992), 57–76 10.4171/ZAA/626 Google Scholar [17] Litvinchuk, G.S.: Boundary Value Problems and Singular Integral Equations with Shift, Nauka, Moscow, 1977 (Russian) Google Scholar [18] Meister, E., Speck, F.–O., and Teixeira, F.: Wiener – Hopf – Hankel Operators for Some Wedge Diffraction Problems with Mixed Boundary Conditions, J. Integr. Equat. and Appl. 4, (2) (1992), 229–255 10.1216/jiea/1181075683 Google Scholar [19] Mikhailov, L.G.: A New Class of Singular Integral Equations and Its Applications to Differential Equations with Singular Coefficients, Trudy Akad. Nauk Tadj. SSR, Vol. 1, 1963 (Transl. in Groningen: Wolters – Noordhoff, 1970) Google Scholar [20] Mikhailov, L.G.: Integral Equations with a Kernel Homogeneous of Degree – 1, Publishing House “Donish”, Dushanbe, 1966 Google Scholar [21] Penzel, F., and Teixeira, F.S.: A Wiener – Hopf Approach for the Scattering by a Disc, Integr. Equat. and Oper. Theory 24, (2) (1996), 230–247 10.1007/BF01193461 Web of Science®Google Scholar [22] Power, S.: The Essential Spectrum of a Hankel Operator with Piecewise Continuous Symbol, Michigan Math. J. 25 (1978), 117–121 10.1307/mmj/1029002010 Web of Science®Google Scholar [23] Santos, P.A., and Teixeira, F.S.: Soomerfeld Half – Plane Problems with Higher Order Boundary Conditions, Math. Nachr. 171 (1995), 269–282 10.1002/mana.19951710116 Web of Science®Google Scholar [24] Teixeira, F.: On a Class of Hankel Operators: Fredholm Properties and Invertibility, Integr. Equat. and Oper. Theory 12 (1989), 592–613 10.1007/BF01199460 Web of Science®Google Scholar [25] Teixeira, F.: Diffraction by a Rectangular Wedge: Wiener – Hopf – Hankel Formulation, Integr. Equat. and Oper. Theory 14 (1991), 436–454 10.1007/BF01218506 Web of Science®Google Scholar Citing Literature Volume217, Issue1September 2000Pages 75-103 ReferencesRelatedInformation

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