Geodesic
Unconditional convergence for wavelet frame extensions
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 45, Tome 456 (2017), pp. 135-143 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Let $\{\psi_{j,k}\}_{(j,k)\in\mathbb Z^2}$, $\{\widetilde\psi_{j,k}\}_{(j,k)\in\mathbb Z^2}$ be dual wavelet frames in $L_2(\mathbb R)$, let $\eta$ be an even, bounded, decreasing on $[0,\infty)$ function such that $$ \int_0^\infty\eta(x)\ln(1+x)\,dx<\infty, $$ and $|\psi(x)|,|\widetilde\psi(x)|\le\eta(x)$. Then the series $\sum_{j,k\in\mathbb Z}(f,\widetilde\psi_{j,k})\psi_{j,k}$ converges unconditionally in $L_p(\mathbb R)$, $1. 
@article{ZNSL_2017_456_a10,
     author = {E. A. Lebedeva},
     title = {Unconditional convergence for wavelet frame extensions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {135--143},
     year = {2017},
     volume = {456},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_456_a10/}
}
TY  - JOUR
AU  - E. A. Lebedeva
TI  - Unconditional convergence for wavelet frame extensions
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2017
SP  - 135
EP  - 143
VL  - 456
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2017_456_a10/
LA  - ru
ID  - ZNSL_2017_456_a10
ER  - 
%0 Journal Article
%A E. A. Lebedeva
%T Unconditional convergence for wavelet frame extensions
%J Zapiski Nauchnykh Seminarov POMI
%D 2017
%P 135-143
%V 456
%U http://geodesic.mathdoc.fr/item/ZNSL_2017_456_a10/
%G ru
%F ZNSL_2017_456_a10
E. A. Lebedeva. Unconditional convergence for wavelet frame extensions. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 45, Tome 456 (2017), pp. 135-143. http://geodesic.mathdoc.fr/item/ZNSL_2017_456_a10/

[1] P. G. Casazza, O. Christensen, “Hilbert space frames containing Riesz basis and Banach spaces which have no subspace isomorphic to $c_0$”, J. Math. Anal. Appl., 202 (1996), 940–950 | DOI | MR | Zbl

[2] O. Christensen, An Introduction to Frames and Riesz Bases. Applied and Numerical Harmonic Analysis, Birkhäuser–Boston, 2016 | MR

[3] G. Gripenberg, “Wavelet bases in $L_p(\mathbb R)$”, Studia Math, 106:2 (1993), 175–187 | DOI | MR | Zbl

[4] I. Dobeshi, Desyat lektsii po veivletam, NITs “Regulyarnaya i khaoticheskaya dinamika”, Izhevsk, 2001

[5] E. M. Dynkin, B. P. Osilenker, “Vesovye otsenki singulyarnykh integralov i ikh prilozheniya”, Itogi nauki i tekhn. Ser. Mat. anal., 21, 1983, 42–129 | MR | Zbl

[6] T. Fiegel, P. Wojtaszczyk, “Special bases in functional spaces”, Handbook of the Geometry of Banach Spaces, v. 1, 2001, 561–597 | DOI | MR

[7] B. S. Kashin, A. A. Saakyan, Ortogonalnye ryady, ATsT, 1999 | MR

[8] A. Krivoshein, V. Protasov, M. Skopina, Multivariate wavelet frames, Springer, Singapore, 2016 | MR | Zbl

[9] Y. Meyer, Wavelets and Operators, Cambridge University Press, Cambridge, MA, 1992 | MR | Zbl

[10] I. Ya. Novikov, V. Yu. Protasov, M. A. Skopina, Teoriya vspleskov, Fizmatlit, 2005 | MR

[11] P. Wojtaszczyk, A Mathematical Introduction to Wavelets, Cambridge University Press, Cambridge, MA, 1997 | MR | Zbl

[12] P. Wojtaszczyk, “Wavelets as unconditional bases in $L_p(\mathbb R)$”, J. Fourier Anal., 5:1 (1999), 73–85 | DOI | MR | Zbl