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Über ein Transmissionsproblem mit Integro-Differentialbedingungen

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Abstract

In this paper we consider the problem of finding certain holomorphic functions defined on ℂ∖iR. These functions are to be such that for both the regions Re z>0 and Re z<0 they assume almost everywhere on iR boundary values which satisfy prescribed coupling conditions which are integro-differential in form. We associate with the problem a transmission operator T and give necessary and sufficient conditions in order that it should be a Fredholm operator. We then construct a bounded left- and right-regularizer for T.

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Literatur

  1. AGMON, S.: Elliptic boundary value problems, New York: American Book, Van Nostrand, Reinhold 1965

    Google Scholar 

  2. GAKHOV, F. D.: Boundary value problems, Oxford: Pergamon Press 1966

    Google Scholar 

  3. GELFAND, I. M. et al.: Kommutative normierte Algebren, Berlin: VEB Deutscher Verlag der Wissenschaften 1964

    Google Scholar 

  4. HOFFMAN, K.: Banach spaces of analytic functions, Englewood Cliffs (N. J.): Prentice-Hall 1962

    Google Scholar 

  5. KRIKUNOV, Yu. M.: On the solution of the generalized Riemann boundary value problem and a linear singular integro-differential equation. Uch. zap. Kazan. univ.112, 191–199 (1952)

    Google Scholar 

  6. LAVOINE, J.: Transformation de Fourier des pseudofunctions avec tables de nouvelles transformées, Paris: Centre National de la Recherche scientifique 1963

    Google Scholar 

  7. MAGNARADZE, L. G.: Theory of a class of linear singular integro-differential equations. Soobshch. Akad. Nauk Gruz. SSR6, 103–110 (1943)

    Google Scholar 

  8. MEISTER, E.: Das Riemannsche Randwertproblem, Ergebnisse und Anwendungen. In: LAUGWITZ, D.: Überblicke Mathematik, Band 6, Zürich: BI, Wissenschaftsverlag 1973

    Google Scholar 

  9. NATANSON, I. P.: Theorie der Funktionen einer reellen Veränderlichen, Berlin: Akademie Verlag 1961

    Google Scholar 

  10. NERI, U.: Singular integrals, Berlin: Springer-Verlag (Lecture Notes in Mathematics, Bd. 200) 1971

    Google Scholar 

  11. RAKOWSTSCHIK, L. S.: Zur Theorie der Integralgleichungen vom Faltungstyp. Usp. Mat. Nauk112, 171–178 (1963)

    Google Scholar 

  12. ROGOZHIN, V. S.: A new integral representation of a sectionally-analytic function and its application. Dokl. Akad. Nauk SSSR135, 791–793 (1960)

    Google Scholar 

  13. VEKUA, I. N.: On one linear Riemann boundary value problem. Trudy Tbil. matem. inst.XI, 109–139 (1942)

    Google Scholar 

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  1. Fachbereich Mathematik der Technischen Hochschule, Schloßgartenstraße 7, D-6100, Darmstadt

    Jörg Donig

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  1. Jörg Donig
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Donig, J. Über ein Transmissionsproblem mit Integro-Differentialbedingungen. Manuscripta Math 23, 1–18 (1977). https://doi.org/10.1007/BF01168583

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  • DOI: https://doi.org/10.1007/BF01168583

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