Abstract
The aim of this work is to provide an efficient method to realize constructively approximate duals of Gabor frames with multivariate atoms. The proposed method is independent of the number of atoms needed and it is applicable also in the case of non-separable atoms. Due to the small number of atoms used in the construction the method is computationally inexpensive.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
A. Bourouihiya, The tensor product of frames. Sampl. Theory Signal Image Process., Int. J. 7(1), 65–76 (2008)
O. Christensen, An Introduction to Frames and Riesz Bases. Applied and Numerical Harmonic Analysis (Birkhäuser, Boston, 2003)
M.A. de Gosson, D. Onchis, Multivariate symplectic Gabor frames with Gaussian windows. Preprint (2013)
H.G. Feichtinger, A. Grybos, D. Onchis, Fast approximation of dual Gabor atoms by masking the adjoint lattice. Preprint
K. Gröchenig, Foundations of Time-Frequency Analysis. Appl. Numer. Harmon. Anal. (Birkhäuser, Boston, 2001)
Yu.I. Lyubarskii, Frames in the Bargmann space of entire functions, in Entire and Subharmonic Functions (Am. Math. Soc., Providence, 1992), pp. 167–180
D. Onchis, Optimized frames and multi-dimensional challenges in time-frequency analysis. Adv. Comput. Math. (2014). doi:10.1007/s10444-013-9332-1
K. Seip, R. Wallstén, Density theorems for sampling and interpolation in the Bargmann–Fock space. II. J. Reine Angew. Math. 429, 107–113 (1992)
Acknowledgements
The work of the first author of the article has been partially supported by the European Commission grant no. FP7-REGPOT-CT-2011-284595 (HOST). The second author has been partially supported by the Polish Ministry of Science and Higher Education.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Onchis, D.M., Grybos, A. (2015). Approximate Dual M-Frames Constructions: The Gabor Case. In: Mityushev, V., Ruzhansky, M. (eds) Current Trends in Analysis and Its Applications. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-12577-0_74
Download citation
DOI: https://doi.org/10.1007/978-3-319-12577-0_74
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-12576-3
Online ISBN: 978-3-319-12577-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)