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- W4302071229 abstract "We study in various functional spaces the equiconvergence of spectral decompositions of the Hill operator $L= -d^2/dx^2 + v(x), $ $x in [0,pi], $ with $H_{per}^{-1} $-potential and the free operator $L^0=-d^2/dx^2, $ subject to periodic, antiperiodic or Dirichlet boundary conditions. In particular, we prove that $$ |S_N - S_N^0: L^a to L^b | to 0 quad text{if} ;; 1<a leq b< infty, ;; 1/a - 1/b <1/2, $$ where $S_N$ and $S_N^0 $ are the $N$-th partial sums of the spectral decompositions of $L$ and $L^0.$ Moreover, if $v in H^{-alpha} $ with $1/2 < alpha < 1$ and $frac{1}{a}=(3/2)-alpha, $ then we obtain uniform equiconvergence: $|S_N - S_N^0: L^a to L^infty | to 0 $ as $N to infty. $" @default.
- W4302071229 created "2022-10-06" @default.
- W4302071229 creator A5083206513 @default.
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- W4302071229 date "2011-10-31" @default.
- W4302071229 modified "2023-09-23" @default.
- W4302071229 title "Equiconvergence of spectral decompositions of Hill-Schrodinger operators" @default.
- W4302071229 doi "https://doi.org/10.48550/arxiv.1110.6696" @default.
- W4302071229 hasPublicationYear "2011" @default.
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