Abstract
Operators which localise both in time and frequency are constructed. They restrict to a finite time interval and cut off low as well as high frequencies (band-pass filters). Explicit expressions for eigenvalues and eigenfunctions (Laguerre functions) are given.
Keywords
MathematicsLaguerre polynomialsEigenfunctionEigenvalues and eigenvectorsInterval (graph theory)Mathematical analysisPhase (matter)Space (punctuation)Pure mathematicsCombinatorics
Affiliated Institutions
Related Publications
Time-frequency localization operators: a geometric phase space approach
The author defines a set of operators which localize in both time and frequency. These operators are similar to but different from the low-pass time-limiting operator, the singu...
Improved Pauli Hamiltonian for local-potential problems
A recently published scheme for obtaining an approximate solution of the Dirac-Hartree-Fock equations for an atom is adapted and applied to the related Dirac-Slater problem. For...
An efficient internally contracted multiconfiguration–reference configuration interaction method
A new internally contracted direct multiconfiguration–reference configuration interaction (MRCI) method is described which allows the use of much larger reference spaces than an...
Theory for the dynamics of clusters near the critical point. I. Relaxation of the Glauber kinetic Ising model
A semiphenomenological cluster theory is developed for dynamic critical properties, which is not limited to small deviations from equilibrium. Explicit numerical expressions are...
Pattern formation outside of equilibrium
A comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium is presented, with emphasis on comparisons between theory and quantitative exp...
Publication Info
- Year
- 1988
- Type
- article
- Volume
- 4
- Issue
- 3
- Pages
- 661-680
- Citations
- 167
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
167
OpenAlex
Cite This
Ingrid Daubechies,
T. Paul
(1988).
Time-frequency localisation operators-a geometric phase space approach: II. The use of dilations.
Inverse Problems
, 4
(3)
, 661-680.
https://doi.org/10.1088/0266-5611/4/3/009
Identifiers
- DOI
- 10.1088/0266-5611/4/3/009