Advertisement

Annali di Matematica Pura ed Applicata

, Volume 91, Issue 1, pp 69–77 | Cite as

Self-adjoint boundary value problems with infinitely many boundary points

  • Allan M. Krall
Article

Summary

The system\(Ly = y' + Py = f,\sum\limits_{i = 0}^m {A_i y(a_i ) = 0} \) is disvussed when it is self-adjoint under a transformation T. In an appropriate Hilbert space its eigenfunction expansion is derived.

Keywords

Boundary Point Fundamental Matrix Adjoint Equation Classical Sense Eigenfunction Expansion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. [1]
    G. A. Bliss,A boundary value problem for a system of ordinary differential equations of the first order, Trans. Amer. Math. Soc.,28 (1926), pp. 561–584.zbMATHMathSciNetCrossRefGoogle Scholar
  2. [2]
    E. A. Coddington -N. Levinson,Theory of Ordonary Differential Equations, McGraw-Hill, New York (1955).Google Scholar
  3. [3]
    G. B. Green -A. M. Krall,Linear differential systems with infinitely many boundary points, Annali di Mat., 91 (1972), pp. 53–67.zbMATHMathSciNetGoogle Scholar
  4. [4]
    A. M. Krall,Boundary value problems with interior point boundary conditions, Pacific J. Math.,29 (1969), pp. 161–166.zbMATHMathSciNetGoogle Scholar
  5. [5]
    W. S. Loud,Self-adjoint multipoint boundary value problems, Pacific J. Math.,20 (1968), pp. 303–317.MathSciNetGoogle Scholar
  6. [6]
    W. T. Reid,A class of two point boundary value problems, Illinois J. Math.,2 (1958), pp. 434–453.zbMATHMathSciNetGoogle Scholar
  7. [7]
    J. S. W. Wong,Some remarks on hermitian and antihermitian properties of Green matrices, S.I.A.M. J. App. Math.,17 (1969), pp. 615–623.zbMATHCrossRefGoogle Scholar
  8. [8]
    A. Zettl,The lack of self-adjointness in three point boundary value problems, Proc. Amer. Math. Soc.,17 (1966), pp. 368–371.zbMATHMathSciNetCrossRefGoogle Scholar
  9. [9]
    A. Zettl,Adjoint and self-adjoint boundary value problems with interface conditions, S.I.A.M. J. App. Math.,16 (1968), pp. 851–859.zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Nicola Zanichelli Editore 1971

Authors and Affiliations

  • Allan M. Krall
    • 1
  1. 1.McAllister BuildingThe Pennsylvania State UniversityUniversity Park

Personalised recommendations