Eigenfunction Expansion and Spectral Theorem

Authors

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

DOI:

https://doi.org/10.32628/IJSRST52310634

Keywords:

Matrix differential operator, Spectral theorem, Convergence theorem.

Abstract

In this present paper, the theory of eigenfunction expansions associated with the second-order differential equations and their spectral behavior.

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. Bhagat, B., ‘Eigenfunction expansions associated with a pair of second order differential equations. Proc. National Inst. Sciences of India Vol. 35, A.No.1 (1969).
  4.  Bhagat, B., ‘Some problems on a pair of singular second order differential equations. Ibid 35A (1969): 232-44.
  5. Bhagat, B., ‘A spectral theorem for a pair of second order singular differential equations, Quart. J. Math. Oxford 21,(1970) 487-95.
  6. Bhagat, B., ‘An equiconvergence theorem for a pair of second order differential equations’. Proc. Amer. Math. Soc. (36), 1 (1972). 144-50.
  7. Bhagat, B., ‘Some Asymptotic formulae’. J. Pure and Appl. Math. India (to appear in vol.5).
  8. Bhagat, B., ‘ On Uniqueness of the Green’s Matrix associated with a pair of second order differential equations’ J. Pure and Appl. Math. India (to appear in vol.5).
  9. Bhagat, B., ‘Ph.D. Thesis’. Patna University. 1966.

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Published

2024-02-29

Issue

Section

Research Articles

How to Cite

[1]
Rajeev Ranjan "Eigenfunction Expansion and Spectral Theorem" International Journal of Scientific Research in Science and Technology(IJSRST), Online ISSN : 2395-602X, Print ISSN : 2395-6011,Volume 11, Issue 1, pp.280-285, January-February-2024. Available at doi : https://doi.org/10.32628/IJSRST52310634