Abstract
Let f∈L p (R), 1≤p≤t8, and c j be the inner product of f and the Hermite function h j . Assume that c j 's satisfy \(\left| {c_j } \right| \cdot f = o\left( 1 \right)\;\quad as\;j \to \infty \) If r=5/4, then the Hermite series Σc j h j conerges to f almost everywhere. If r=9/4-1/p, the Σ c j h j converges to f in L p (R).
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Lin, CC. Summability of Hermite Series. Analysis in Theory and Applications 17, 45–53 (2001). https://doi.org/10.1023/A:1015510013983
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DOI: https://doi.org/10.1023/A:1015510013983