Abstract
We analyze the uniform convergence of the Fourier series expansions of Hölder functions in the system of eigenfunctions of a spectral problem with squared spectral parameter in a boundary condition. To this end, we first prove a theorem on the equiconvergence of such expansions with those in a well-known orthonormal basis.
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References
Kapustin, N.Yu., On a Spectral Problem in the Theory of the Heat Operator, Differ. Uravn., 2009, vol. 45, no. 10, pp. 1509–1511.
Kapustin, N.Yu. and Moiseev, E.I., On Spectral Problems with Spectral Parameter in a Boundary Condition, Differ. Uravn., 1997, vol. 33, no. 1, pp. 115–119.
Moiseev, E.I. and Kapustin, N.Yu., On the Basis Property in the Space Lp of Systems of Eigenfunctions Corresponding to Two Problems with Spectral Parameter in a Boundary Condition, Differ. Uravn., 2000, vol. 36, no. 10, pp. 1357–1360.
Moiseev, E.I. and Kapustin, N.Yu., Convergence of Spectral Expansions of Hölder Functions for Two Problems with Spectral Parameter in a Boundary Condition, Differ. Uravn., 2000, vol. 36, no. 8, pp. 1069–1074.
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Original Russian Text © N.Yu. Kapustin, 2010, published in Differentsial’nye Uravneniya, 2010, Vol. 46, No. 10, pp. 1504–1507.
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Kapustin, N.Y. On the uniform convergence of the Fourier series for a spectral problem with squared spectral parameter in a boundary condition. Diff Equat 46, 1507–1510 (2010). https://doi.org/10.1134/S0012266110100150
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DOI: https://doi.org/10.1134/S0012266110100150