First-Order Operator Equations

  • Aleksei A. Dezin
Part of the Springer Series in Soviet Mathematics book series (SSSOV)


This chapter is, in a definite sense, central to our entire exposition. Here, by using the simplest entities, operator equations of the first order, generated by special classes of boundary value problems for partial differential equations that originate from the constructions and results presented above, we consider the whole circle of ideas that are of interest. In passing to more complicated entities the study of the corresponding questions turns out to involve a whole series of difficulties of a technical nature, whereas the constructions in this chapter are as transparent and elementary as possible. Let t∈ (0, b) =V t , ℍ t ≡ℍ t (V t ) the corresponding Hilbert space, and D t : ℍt→ℍt, any of the operators generated by the Operation Dt. Then by an operator equation (or differential-operator equation) of the first order we ordinarily understand an equation of the form

Lu ≡ (A0Dt+ A1)u=f


Cauchy Problem Operator Equation Proper Operator Point Spectrum Differential Property 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Aleksei A. Dezin
    • 1
  1. 1.Steklov Mathematical InstituteMoscowUSSR

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