Geodesic
Nonlinear $N$-term approximation by refinable functions
Algebra i analiz, Tome 16 (2004) no. 1, pp. 163-206.

Voir la notice de l'article provenant de la source Math-Net.Ru

@article{AA_2004_16_1_a5,
     author = {Yu. A. Brudnyi},
     title = {Nonlinear $N$-term approximation by refinable functions},
     journal = {Algebra i analiz},
     pages = {163--206},
     publisher = {mathdoc},
     volume = {16},
     number = {1},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AA_2004_16_1_a5/}
}
TY  - JOUR
AU  - Yu. A. Brudnyi
TI  - Nonlinear $N$-term approximation by refinable functions
JO  - Algebra i analiz
PY  - 2004
SP  - 163
EP  - 206
VL  - 16
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AA_2004_16_1_a5/
LA  - ru
ID  - AA_2004_16_1_a5
ER  - 
%0 Journal Article
%A Yu. A. Brudnyi
%T Nonlinear $N$-term approximation by refinable functions
%J Algebra i analiz
%D 2004
%P 163-206
%V 16
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AA_2004_16_1_a5/
%G ru
%F AA_2004_16_1_a5
Yu. A. Brudnyi. Nonlinear $N$-term approximation by refinable functions. Algebra i analiz, Tome 16 (2004) no. 1, pp. 163-206. http://geodesic.mathdoc.fr/item/AA_2004_16_1_a5/

[Ва] Bandt C., “Self-similar sets. 5. Integer matrices and fractal tilings $\mathbb R^n$”, Proc. Amer. Math. Soc., 112 (1991), 549–562 | DOI | MR | Zbl

[Brl] Brudnyi Yu., “Ratsionalnaya approksimatsiya i teoremy vlozheniya”, Dokl. AN SSSR, 247:2 (1979), 269–272 | MR | Zbl

[Br2] Brudnyi Yu., “Adaptivnaya approksimatsiya funktsii s osobennostyami”, Tr. Mosk. mat. o-va, 55, 1994, 149–242 | MR | Zbl

[Br3] Brudnyi Yu., “Nonlinear piecewise polynomial approximation of functions from Besov spaces”, Math. Balkanica (N.S.), 16:1–4 (2002), 339–358 | MR | Zbl

[BI] Brudnyi Yu., Irodova I., “Nelineinaya splain-approksimatsiya funktsii mnogikh peremennykh i $B$-prostranstva”, Algebra i analiz, 4:4 (1992), 45–79 | MR

[BK] Brudnyi Yu., Kozlova I., “Algoritm nelineinoi approksimatsii kusochnymi polinomami”, Mat. fiz., anal., geom., 9:3 (2002), 311–325 | MR | Zbl

[BK1] Brudnyi Yu., Kruglyak N., “Ob odnom semeistve approksimatsionnykh prostranstv”, Issledovaniya po teorii funktsii mnogikh veschestvennykh peremennykh, 2, Yarosl. gos. un-t, Yaroslavl, 1978, 15–42 | MR | Zbl

[BK2] Brudnyi Yu., Krugljak N., Interpolation functors and interpolation spaces, Vol. 1, North-Holland Math. Library, 47, North-Holland, Amsterdam, 1991 | MR | Zbl

[ВКо] Brudnyi Yu., Kotlyar B., “Odna zadacha kombinatornoi geometrii”, Sib. mat. zh., 11:5 (1970), 1171–1173 | MR | Zbl

[BL] Bergh J., Löfström J., Interpolation spaces. An introduction, Grundlehren Math. Wiss., 223, Springer-Verlag, Berlin–New York, 1976 | MR | Zbl

[BS1] Birman M., Solomyak M., “Kusochno-polinomialnye priblizheniya funktsii klassov $W_p^\alpha$”, Mat. sb., 73(115):3 (1967), 331–355 | MR | Zbl

[BS2] Birman M., Solomyak M., “Otsenki singulyarnykh chisel integralnykh operatorov”, Uspekhi mat. nauk, 32:1(193) (1977), 17–84 | MR | Zbl

[BS3] Birman M., Solomyak M., “Kolichestvennyi analiz v teoremakh vlozheniya Soboleva i prilozheniya k spektralnoi teorii”, 10-ya matematicheskaya shkola, In-t mat. AN UkrSSR, Kiev, 1974, 5–189 | MR

[CDM] Cavaretta A. S., Dahmen W., Miccelli C. A., Stationary subdivisions, Mem. Amer. Math. Soc., 93, no. 453, 1991, 186 pp. | MR

[CGV] Cohen A., Gröchenig K., Villemoes L. F., “Regularity of multivariate refinable functions”, Constr. Approx., 15 (1999), 241–255 | DOI | MR | Zbl

[D] DeVore R. A., “Nonlinear approximation”, Acta Numer., 7, Cambridge Univ. Press, Cambridge, 1998, 51–150 | MR | Zbl

[DJP] DeVore R. A., Jawerth B., Popov V., “Compression of wavelet decompositions”, Amer. J. Math., 114 (1992), 737–785 | DOI | MR | Zbl

[DPY] DeVore R. A., Petrushev P., Yu X. M., “Nonlinear wavelet approximation in the space $C(\mathbb R^d)$”, Progress in Approximation Theory (Tampa, FL, 1990), Springer Ser. Comput. Math., 19, Springer, New York, 1992, 261–283 | MR | Zbl

[H] Hutchinson J. E., “Fractals and self-similarity”, Indiana Univ. Math. J., 30 (1981), 713–747 | DOI | MR | Zbl

[HLR] He X.-G., Lau K.-S., Rao H., “Self-affine sets and graph-directed systems”, Constr. Approx., 19 (2003), 373–397 ; Preprint, City Univ. of Hong-Kong, 2002, 27 pp. | DOI | MR | Zbl

[J] Jia R. Q., Approximation properties of multivariate wavelets, Preprint, Univ. of Alberta, Edmonton, 1996

[JM] Jia R. Q., Micchelli C. A., “On linear independence for integer translates of a finite number of functions”, Proc. Edinburgh Math. Soc. (2), 36 (1993), 69–85 | DOI | MR | Zbl

[L-R] Lemarié-Rieusset P. G., “Projecteurs invariants, matrices de dilatation, ondelettes et analyses multirésolutions”, Rev. Mat. Iberoamericana, 10:2 (1994), 283–347 | MR | Zbl

[LW] Lagarias J. C., Wang Y., “Self-affine tiles in $\mathbb R^n$”, Adv. Math., 121 (1996), 21–49 | DOI | MR | Zbl

[PP] Petrushev P., Popov V., Rational approximation of real functions, Encyclopedia Math. Appl., 28, Cambridge Univ. Press, Cambridge, 1987 | MR | Zbl

[R] Rosen K. H. (ed.), Handbook of discrete and combinatorial mathematics, CRC Press, Boca Raton, FL, 2000 | MR

[S] Schmidt E., “Zur Theorie der linearen und nonlinearen Integralgleichungen. I”, Math. Ann., 63 (1907), 433–476 | DOI | MR | Zbl

[T] Temlyakov V. N., Nonlinear methods of approximation, IMI-Preprint Ser., Univ. of South Caroline, 2001, 1–57 | MR

[W] Wojtaszczyk P., A mathematical introduction to wavelets, London Math. Soc. Student Text, 37, Cambridge Univ. Press, Cambridge, 1997 | MR | Zbl

[Z] Zhou D.-X., “Self-similar lattice tilings and subdivision schemes”, SIAM J. Math. Anal., 33:1 (2001), 1–15, electronic | DOI | MR | Zbl