In this paper, we investigate the structure of dilation operators acting on anisotropic homogeneous Besov spaces B_{p,q}(A) associated with an expansive matrix A \\in GL(d, R). We first establish that the group of dilation matrices compatible with the A-wavelet system coincides with the centralizer of A \\in GL(d, R). We then characterize all matrices C \\in GL(d, R) for which the normalized dilation D_C(f) is bounded on B_{p,q}(A). Finally, we show that D_C induces an isomorphism on B_{p,q}(A) for all parameters (p,q) if and only if the frequency coverings generated by A and by the conjugated matrix A_C are equivalent in the sense of decomposition spaces.
Cheshmavar, J. (2026). CHARACTERIZATION OF DILATION OPERATORS ON ANISOTROPIC BESOV SPACES. Journal of Advanced Mathematical Modeling, 16(1), 115–123. https://doi.org/10.22055/jamm.2026.50713.2417
MLA
Cheshmavar, J. "CHARACTERIZATION OF DILATION OPERATORS ON ANISOTROPIC BESOV SPACES", Journal of Advanced Mathematical Modeling, 16, 1, 2026, 115–123. doi: 10.22055/jamm.2026.50713.2417
HARVARD
Cheshmavar, J. (2026). 'CHARACTERIZATION OF DILATION OPERATORS ON ANISOTROPIC BESOV SPACES', Journal of Advanced Mathematical Modeling, 16(1), pp. 115–123. doi: 10.22055/jamm.2026.50713.2417
CHICAGO
Cheshmavar, J., "CHARACTERIZATION OF DILATION OPERATORS ON ANISOTROPIC BESOV SPACES." Journal of Advanced Mathematical Modeling, 16 1 (2026): 115–123, doi: 10.22055/jamm.2026.50713.2417
VANCOUVER
Cheshmavar J. CHARACTERIZATION OF DILATION OPERATORS ON ANISOTROPIC BESOV SPACES. JAMM. 2026;16(1):115–123 (In Persian). doi: 10.22055/jamm.2026.50713.2417
