Published April 4, 2017
| public
Book Section - Chapter
Local Approximation Using Hermite Functions
Abstract
We develop a wavelet-like representation of functions in Lp(R) based on their Fourier–Hermite coefficients; i.e., we describe an expansion of such functions where the local behavior of the terms characterize completely the local smoothness of the target function. In the case of continuous functions, a similar expansion is given based on the values of the functions at arbitrary points on the real line. In the process, we give new proofs for the localization of certain kernels, as well as for some very classical estimates such as the Markov–Bernstein inequality.
Additional Information
© 2017 Springer International Publishing AG. First Online: 04 April 2017. The research of HNM is supported in part by Grant W911NF-15-1-0385 from the US Army Research Office. We thank the editors for their kind invitation to submit this paper.Additional details
- Eprint ID
- 78946
- Resolver ID
- CaltechAUTHORS:20170711-111543165
- W911NF-15-1-0385
- Army Research Office (ARO)
- Created
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2017-07-11Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field
- Series Name
- Springer Optimization and Its Applications
- Series Volume or Issue Number
- 117