General Theory of The Matrix Differential Operator and Spectral Theorem

Authors

  • Rajeev Ranjan  University Department of Mathematics, J. P. University, Chapra, Bihar, India

Keywords:

Matrix differential operator, Spectral theorem, Convergence theorem.

Abstract

In this present paper, the general theory of the matrix differential operator and spectral theorem has been explained. The theory of eigenfunction expansions associated with the second-order differential equations and their spectral behavior has been also presented in this paper.

References

  1. Titchmarsh, E.C.‘Eigenfunction expansions associated with second order differential equation’ Part I, Oxford 1962
  2. Conte, S. D.andSangren, W.C.‘On asymptotic solution for a pair of singular first order equations’ Proc. Amer. Math. Soc. 4, (1953) 696-702
  3. Hilbert, D., Grundzuge einer allgemeinen theories der linearen Integral-gliechungen, B.G. Teubner, Leipzig and Barlin, (1912), cited as 'Integral Gleichungen'.
  4. Eastham, M.S.P., Theory of ordinary differential equations, von Nostrand Reinhold, London (1970).
  5. Lidskii, V. B., On the number of solutions with integrable square of the system of differential equations - y" + p(t) y = Ay; Doklady Akad. Nauk SSSR. N.S. 95 (1954), 217-20.
  6. Kamke, E., Differential gleichungen, Auflage Akademiache Verlag sgesllschaft Becker and Frler kem. Cas. Leipzig (1943).
  7. Y.P.Pandey, A.Kumar, A spectral theorem for a pair of singular matrix differential equations, In; Proc. math. Sci. BHU, India 3 (1987), 201-212.
  8. Chakravarty, N.K., Some problems in Eigenfunction expansions (1), Quart. J.Math., (16) 62 (1965), 135-50.
  9. Chakravarty, N.K., Ibid (II) 19 (1968), 213-24.
  10. Chakravarty, N.K., Ibid (III), Ibid 397-415.
  11. Chakravarty, N.K., Ibid (IV) Indian J.Pure and Appl. Math(1) 3 (1970), 347-53.
  12. Roos, B.W. and Sangren, W.C., Asymptatic solutions and an equi-convergence theorem for a pair of first order differential equations, J.Soc. Indust. Appl. Math. (2), 11 (1963), 421-30.
  13. Bhagat, B.‘A spectral theorem for a pair of second order singular differential equations’ Quart. J. Math. Oxford 21, (1970), 487-495.

Downloads

Published

2023-12-30

Issue

Section

Research Articles

How to Cite

[1]
Rajeev Ranjan, " General Theory of The Matrix Differential Operator and Spectral Theorem, International Journal of Scientific Research in Science and Technology(IJSRST), Online ISSN : 2395-602X, Print ISSN : 2395-6011, Volume 10, Issue 6, pp.517-520, November-December-2023.