zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Multiwavelet frames from refinable function vectors. (English) Zbl 1059.42030
A $d$-refinable function vector $\phi = (\phi_1, \ldots, \phi_r)^T$ satisfies the refinement equation $$ \phi = \vert d\vert \sum_{k \in {\Bbb Z}} a_k \phi(d\cdot - k), $$ where $r$ is the multiplicity, $d$ the dilation factor, and $a$ is the finitely supported sequence of $r\times r$ matrices. Such a vector generates a wavelet function vector by $$ \widehat \psi^l (d \xi) = b^l(\xi) \widehat \phi(\xi), $$ where $l=1, \ldots, L$ and $b^l$ are periodic trigonometric polynomials. The paper under review studies the properties of dual wavelet frames and of wavelet frames generated by refinable function vectors. In particular, algorithms for constructing dual wavelet frames with maximum vanishing moments are given. Moreover, symmetry/antisymmetry properties of wavelets are examined and examples are provided.

42C40Wavelets and other special systems
42C15General harmonic expansions, frames
Full Text: DOI