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Spectral Analysis of Four Term Differential Operator
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  • Journal title : Kyungpook mathematical journal
  • Volume 50, Issue 1,  2010, pp.15-35
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2010.50.1.015
 Title & Authors
Spectral Analysis of Four Term Differential Operator
Oluoch, Nyamwala Fredrick;
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 Abstract
By strengthening dichotomy condition and weakening decay conditions, we show that a four term 2n-th order differential operator with unbounded coefficients is nonlimit-point. Using stringent conditions we show that the deficiency index of this operator is determined by the behaviour of the coefficients themselves. Similarly, we prove the absence of singular continuous spectrum and that the absolutely continuous spectrum has multiplicity two.
 Keywords
differential operators;deficiency indices;absolutely continuous;spectrum;eigenvalues;
 Language
English
 Cited by
 References
1.
H. Behncke, The Spectrum of Differential Operators with Almost Constant Coefficients II, J. Comput. Appl.Math., 148(2002), 287-305. crossref(new window)

2.
H. Behncke, A Spectral Theory of Higher Order Differential Operators, Proc. London Math. Soc., 92(3)(2006), 139-160.

3.
H. Behncke, The Remainder in Asymptotic Integration II, to appear in Proc. Amer. Math. Soc.

4.
H. Behncke and D. B. Hinton, Eigenfunctions, Deficiency Indices and Spectra of Odd Order Differential Operators, Proc. London Math. Soc., (3) 97(2008), 425-449. crossref(new window)

5.
H. Behncke and C. Remling, Asymptotic Integration of Linear Differential Equations, J. Math. Anal. Appl., 210(1997), 585-597. crossref(new window)

6.
H. Behncke and C. Remling, Uniform Asymptotic Integration of a Family of Linear Differential System, Math. Nachr., 225(2001), 5-17. crossref(new window)

7.
H. Behncke, D. Hinton, and C. Remling, The Spectrum of Differential Operators of Order 2n with Almost Constant Coefficients, Differential Equations, 175(2001), 130-162. crossref(new window)

8.
M. S. P. Eastham, The Deficiency Index of Even Order Differential Equations, J. London Math. Soc., 26(1982), 113-116. crossref(new window)

9.
M. S. P. Eastham, Repeated Diagonalization and Extended Liouville-Green asymptotic Formulae, J. London Math. Soc., (2) 36(1987), pp 115. crossref(new window)

10.
M. S. P. Eastham, The Asymptotic Solutions of Linear Differential Systems, London Math. Soc., Monographs New Series (Oxford University Press, Oxford), 1989.

11.
W. N. Everitt and D. Race, Some Remarks on Linear Ordinary quasi-differential Expressions, Proc. London Math. Soc., (3) 54(1987), 300-320. crossref(new window)

12.
A. P. Griffiths, Introduction to Algebraic Curves, American Mathematic Soc., Beijing University Press., Beijing., 1989.

13.
D. B. Hinton and A. Schneider, On the Titchmarsh-Weyl Coefficients for Singular S-Hermitian Systems I, Math. Nachr., 163(1993), 323-342. crossref(new window)

14.
D. B. Hinton and J. K. Shaw, On the Titchmarsh-Weyl M($\lambda$)-Functions for Linear Hamiltonian Systems, J. Differential Equations, 40(1981), 316-342. crossref(new window)

15.
C. Remling, Spectral Analysis of Higher Order Differential operator I, general properties of the M-Functions, J. London. Math. Soc., 58(2)(1998), 367-380. crossref(new window)

16.
C. Remling, Spectral Analysis of Higher Order Differential operator II, Fourth Order Equations, J. London Math. Soc., 59(2)(1999), 188-206. crossref(new window)

17.
P. W. Walker, A Vector-Matrix Formulation for Formally Symmetric Ordinary Differential Equations with Applications to Solutions of Integrable Square, J. London Math. Soc., 9(1974), 151-159. crossref(new window)

18.
J. Weidmann, Spectral Theory of Ordinary Differential Operators, Springer Lect. Notes, 1258, Springer-Verlag, Berlin, 1987.