zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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)
Connection coefficients of Shannon wavelets. (English) Zbl 1117.65179

The paper presents an explicit computation of the matrix coefficients representing differential operators of arbitrary order in a Shannon wavelet basis. Shannon wavelets for which explicit expressions are available in physical and in Fourier space form an orthogonal basis of L 2 (). They are compactly supported in Fourier space, exhibit a 1/x decay in physical space and they can be derived from harmonic wavelets. The entries of the stiffness matrix required e.g. for Galerkin discretizations of differential equations fulfill recursion formulas.

In the present paper they are called connection coefficients, in the literature, however, this expression is used for the coefficients representing bilinear terms in a wavelet basis, i.e. the projection of the square of a wavelet onto a wavelet.

MSC:
65T60Wavelets (numerical methods)
65M60Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)
94A11Application of orthogonal and other special functions in communication
42C40Wavelets and other special systems