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Article Dans Une Revue Journal of Mathematical Analysis and Applications Année : 2022

Homogeneous Dirichlet wavelets on the interval diagonalizing the derivative operator, and related applications

Résumé

This paper presents a new construction of a homogeneous Dirichlet wavelet basis on the unit interval, linked by a diagonal differentiation-integration relation to a standard biorthogonal wavelet basis. This allows to compute the solution of Poisson equation by renormalizing the wavelet coefficients - as in Fourier domain but using locally supported basis functions with boundary conditions-, which yields a linear complexity $O(N)$ for this problem. Another application concerns the construction of free-slip divergence-free wavelet bases of the hypercube, in general dimension, with an associated decomposition algorithm as simple as in the periodic case.
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Dates et versions

hal-01568431 , version 1 (25-07-2017)
hal-01568431 , version 2 (12-03-2018)
hal-01568431 , version 3 (15-02-2019)

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Souleymane Kadri Harouna, Valérie Perrier. Homogeneous Dirichlet wavelets on the interval diagonalizing the derivative operator, and related applications. Journal of Mathematical Analysis and Applications, 2022, 505 (2), pp.125479. ⟨10.1016/j.jmaa.2021.125479⟩. ⟨hal-01568431v3⟩
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