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Spectral Analysis and Representations of Solutions of Abstract Integro-differential Equations in Hilbert Space

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Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 236))

Abstract

We study an abstract integro-differential equations with unbounded operator coefficients in Hilbert space. We obtain the expansion of the strong solutions of such type equations as the exponential series corresponding to the spectra of operator-functions which are the symbols of these equations.

Mathematics Subject Classification (2010). Primary 34D05; Secondary 34C23.

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Author information

Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow Lomonosov State University, Vorobievi Gori, Moscow, 117234, Russia

    Victor V. Vlasov & Nadezda A. Rautian

Authors
  1. Victor V. Vlasov
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  2. Nadezda A. Rautian
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Corresponding author

Correspondence to Victor V. Vlasov .

Editor information

Editors and Affiliations

  1. Departamento de Análisis Matemático, Universidad de Sevilla, Sevilla, Spain

    Manuel Cepedello Boiso

  2. Department of Mathematics, The Royal Institute of Technology, Stockholm, Sweden

    Håkan Hedenmalm

  3. Department of Mathematics & Computer Sci, Free University Amsterdam, Amsterdam, The Netherlands

    Marinus A. Kaashoek

  4. Departamento de Análisis Matemático, Universidad de Sevilla, Sevilla, Spain

    Alfonso Montes Rodríguez

  5. Department of Mathematics, Brown University, Providence, Rhode Island, USA

    Sergei Treil

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Vlasov, V.V., Rautian, N.A. (2014). Spectral Analysis and Representations of Solutions of Abstract Integro-differential Equations in Hilbert Space. In: Cepedello Boiso, M., Hedenmalm, H., Kaashoek, M., Montes Rodríguez, A., Treil, S. (eds) Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation. Operator Theory: Advances and Applications, vol 236. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0648-0_33

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