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)
Optimal cylindrical and spherical Bessel transforms satisfying bound state boundary conditions. (English) Zbl 0927.65102
Summary: Optimal discrete transforms based upon the radial Laplacian eigenfunctions in cylindrical and spherical coordinates are presented, featuring the following properties: (1) bound state boundary conditions are enforced; (2) in the case of cylindrical or spherical symmetry, the relevant discrete Bessel transform (DBT) is analogous to the discrete Fourier transform in Cartesian coordinates; (3) the underlying quadrature algorithms achieve a Gaussian-like accuracy; (4) orthogonality of the transform can be ensured even in the absence of symmetry. Efficient multidimensional pseudospectral schemes are thus enabled in either direct or nondirect product representations. The illustrative program computes the various DBTs and applies them to the eigenvalue calculation for the two- and three-dimensional harmonic oscillator.
MSC:
65L15Eigenvalue problems for ODE (numerical methods)
65N25Numerical methods for eigenvalue problems (BVP of PDE)
35P15Estimation of eigenvalues and upper and lower bounds for PD operators
34L10Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions (ODE)
65T50Discrete and fast Fourier transforms (numerical methods)