- Author
- Stevan Pilipović, Dušan Rakić, Nenad Teofano and Jasson Vindas Diaz (UGent)
- Organization
- Project
- Abstract
- We describe local and global behavior of wavelet transforms of ultradifferentiable functions. The results are given in the form of continuity properties of the wavelet transform on Gelfand–Shilov type spaces and their dual spaces. In particular, we introduce a new family of highly time-scale localized spaces on the upper half-space. We study the wavelet synthesis operator (the left-inverse of the wavelet transform) and obtain the resolution of identity (Calderón reproducing formula) in the context of ultradistributions.
- Keywords
- Calderón reproducing formula, Gelfand–Shilov spaces, Ultradistributions, Wavelet transform, PSEUDODIFFERENTIAL-OPERATORS, EXPONENTIAL DECAY, EQUATIONS, ULTRADISTRIBUTIONS, EXTENSIONS, THEOREMS
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8049866
- MLA
- Pilipović, Stevan, et al. “The Wavelet Transforms in Gelfand-Shilov Spaces.” COLLECTANEA MATHEMATICA, vol. 67, no. 3, 2016, pp. 443–60, doi:10.1007/s13348-015-0154-y.
- APA
- Pilipović, S., Rakić, D., Teofano, N., & Vindas Diaz, J. (2016). The wavelet transforms in Gelfand-Shilov spaces. COLLECTANEA MATHEMATICA, 67(3), 443–460. https://doi.org/10.1007/s13348-015-0154-y
- Chicago author-date
- Pilipović, Stevan, Dušan Rakić, Nenad Teofano, and Jasson Vindas Diaz. 2016. “The Wavelet Transforms in Gelfand-Shilov Spaces.” COLLECTANEA MATHEMATICA 67 (3): 443–60. https://doi.org/10.1007/s13348-015-0154-y.
- Chicago author-date (all authors)
- Pilipović, Stevan, Dušan Rakić, Nenad Teofano, and Jasson Vindas Diaz. 2016. “The Wavelet Transforms in Gelfand-Shilov Spaces.” COLLECTANEA MATHEMATICA 67 (3): 443–460. doi:10.1007/s13348-015-0154-y.
- Vancouver
- 1.Pilipović S, Rakić D, Teofano N, Vindas Diaz J. The wavelet transforms in Gelfand-Shilov spaces. COLLECTANEA MATHEMATICA. 2016;67(3):443–60.
- IEEE
- [1]S. Pilipović, D. Rakić, N. Teofano, and J. Vindas Diaz, “The wavelet transforms in Gelfand-Shilov spaces,” COLLECTANEA MATHEMATICA, vol. 67, no. 3, pp. 443–460, 2016.
@article{8049866,
abstract = {{We describe local and global behavior of wavelet transforms of ultradifferentiable functions. The results are given in the form of continuity properties of the wavelet transform on Gelfand–Shilov type spaces and their dual spaces. In particular, we introduce a new family of highly time-scale localized spaces on the upper half-space. We study the wavelet synthesis operator (the left-inverse of the wavelet transform) and obtain the resolution of identity (Calderón reproducing formula) in the context of ultradistributions.}},
author = {{Pilipović, Stevan and Rakić, Dušan and Teofano, Nenad and Vindas Diaz, Jasson}},
issn = {{0010-0757}},
journal = {{COLLECTANEA MATHEMATICA}},
keywords = {{Calderón reproducing formula,Gelfand–Shilov spaces,Ultradistributions,Wavelet transform,PSEUDODIFFERENTIAL-OPERATORS,EXPONENTIAL DECAY,EQUATIONS,ULTRADISTRIBUTIONS,EXTENSIONS,THEOREMS}},
language = {{eng}},
number = {{3}},
pages = {{443--460}},
title = {{The wavelet transforms in Gelfand-Shilov spaces}},
url = {{http://doi.org/10.1007/s13348-015-0154-y}},
volume = {{67}},
year = {{2016}},
}
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