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The Dirichlet problem on a half-line

  • Alexander Ya. Shklyar
Chapter
Part of the Operator Theory Advances and Applications book series (OT, volume 92)

Abstract

Let A and B be arbitrary c.n.o. in H. By Lemma 6.1. to each weak solution y(t) of equation (1) on R+ there correspond f0 = y(0) ∈ H and an E-sequence in H \(\{ f_1^{(k)}\} _{k = 1}^\infty \) such that ∀k ≥ 1: f 1 (k) = (E k y)′(0), and
$$y(t) = \begin{array}{*{20}{c}} {\lim } \\ {k \to + \infty } \end{array}({\psi _0}(A,B,t){E_k}{f_0} + {\psi _1}(A,B,t)f_1^k)\,(t \in {R_ + }).$$

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Copyright information

© Birkhäuser Verlag 1997

Authors and Affiliations

  • Alexander Ya. Shklyar
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKievUkraine

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