On the Hermite expansions of functions from the Hardy class

• Autorzy: Rahul Garg , Sundaram Thangavelu
• Języki publikacji: EN

Abstrakty

EN

Considering functions f on ℝⁿ for which both f and f̂ are bounded by the Gaussian $e^{-1/2 a|x|²}$, 0 < a < 1, we show that their Fourier-Hermite coefficients have exponential decay. Optimal decay is obtained for O(n)-finite functions, thus extending a one-dimensional result of Vemuri.

Kategorie tematyczne

• 42B35: Function spaces arising in harmonic analysis
• 42C15: General harmonic expansions, frames
• 42C10: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 198
• Numer: 2
• Strony: 177-195

Daty

wydano

2010

Twórcy

autor

Rahul Garg

• Department of Mathematics, Indian Institute of Science, Bangalore 560 012, India

autor

Sundaram Thangavelu

• Department of Mathematics, Indian Institute of Science, Bangalore 560 012, India

Identyfikatory

DOI

10.4064/sm198-2-5