For logarithmic weights the spaces match Pilipović spaces and Hermite coefficients decay at explicit rates that imply decay for harmonic-oscillator solutions; for other weights the Hermite projections decay exponentially, and a partial improvement is obtained on Vemuri's subcritical Hardy conjecture
23, American Mathematical Soc
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Hermite expansions of functions from the weighted Hardy class
For logarithmic weights the spaces match Pilipović spaces and Hermite coefficients decay at explicit rates that imply decay for harmonic-oscillator solutions; for other weights the Hermite projections decay exponentially, and a partial improvement is obtained on Vemuri's subcritical Hardy conjecture