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)
Approximation order provided by refinable function vectors. (English) Zbl 0870.41015
Summary: In this paper we consider L p -approximation by integer translates of a finite set of functions ϕ ν (ν=0,,r-1) which are not necessarily compactly supported, but have a suitable decay rate. Assuming that the function vector ϕ=(ϕ ν ) ν=0 r-1 is refinable, necessary and sufficient conditions for the refinement mask are derived. In particular, if algebraic polynomials can be exactly reproduced by integer translates of ϕ ν , then a factorization of the refinement mask of ϕ can be given. This result is a natural generalization of the result for a single function ϕ, where the refinement mask of ϕ contains the factor ((1+e -iu )/2) m if approximation order m is achieved.

41A25Rate of convergence, degree of approximation
41A30Approximation by other special function classes
42A99Fourier analysis in one variable
46C99Inner product spaces, Hilbert spaces