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Initial data of solutions

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

Abstract

Let A and B be c.n.o. in H such that P = σ(A, B) satisfies (2). By virtue of Statement 5.1, this means that the Cauchy problem for equation (1) on R+ is well-posed in G = D(B) x (D(A) ∩D(|B|1/2)). In other words, for any (f0, f1) ∈ D(B) x (D(A)∩D(|B|1/2)) there exists a unique solution of equation (1) on R+ such that \(y(0) = {f_0},y'(0) = {f_1}.\)

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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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