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Resolvent Operators for Some Classes of Integro-Differential Equations

In: Mathematical Analysis, Approximation Theory and Their Applications

Author

Listed:
  • I. N. Parasidis

    (Department of Electrical Engineering)

  • E. Providas

    (Department of Mechanical Engineering)

Abstract

Explicit representations are constructed for the resolvents of the operators of the form B = A ̂ + Q 1 $$B =\widehat{ A} + Q_{1}$$ and B = A ̂ 2 + Q 2 $$\mathbf{B} =\widehat{ A}^{2} + Q_{2}$$ , where A ̂ $$\widehat{A}$$ and A ̂ 2 $$\widehat{A}^{2}$$ are linear closed operators with known resolvents and Q 1 and Q 2 are perturbation operators embedding inner products of A ̂ $$\widehat{A}$$ and A ̂ 2 $$\widehat{A}^{2}$$ as they appear in integro-differential equations and other applications.

Suggested Citation

  • I. N. Parasidis & E. Providas, 2016. "Resolvent Operators for Some Classes of Integro-Differential Equations," Springer Optimization and Its Applications, in: Themistocles M. Rassias & Vijay Gupta (ed.), Mathematical Analysis, Approximation Theory and Their Applications, pages 535-558, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-31281-1_24
    DOI: 10.1007/978-3-319-31281-1_24
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