Uniform Convergence of Fourier Series Expansions for a Fourth-Order Spectral Problem with Boundary Conditions Depending on the Eigenparameter

Abstract

In this paper, we consider the eigenvalue problem for ordinary differential equations of fourth order with a spectral parameter contained in two of boundary conditions. We obtain refined asymptotic formulas for eigenvalues and eigenfunctions, and study uniform convergence of Fourier series expansions of continuous functions in the system of eigenfunctions of this problem.

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Acknowledgements

The author would like to thank the reviewers for their valuable comments and wishes on the paper.

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Correspondence to Faiq Mirzali Namazov.

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Communicated by Majid Gazor.

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Namazov, F.M. Uniform Convergence of Fourier Series Expansions for a Fourth-Order Spectral Problem with Boundary Conditions Depending on the Eigenparameter. Bull. Iran. Math. Soc. 47, 225–235 (2021). https://doi.org/10.1007/s41980-020-00378-6

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Keywords

  • Eigenvalue problem
  • Ordinary differential equations of fourth order
  • Eigenfunction
  • Spectral expansion
  • Uniform convergence

Mathematics Subject Classification

  • 34B05
  • 34B24
  • 34L10
  • 34L20
  • 34B08
  • 34L15