6533b7defe1ef96bd12765a7
RESEARCH PRODUCT
Inversion Formulas for the Discretized Hilbert Transform on the Unit Circle
Claus B. Schneidersubject
Numerical AnalysisHilbert manifoldDiscretizationHilbert R-treeApplied MathematicsMathematical analysisSingular integralHilbert–Huang transformComputational Mathematicssymbols.namesakeUnit circlesymbolsHilbert transformMoore–Penrose pseudoinverseMathematicsdescription
A discrete version of the Hilbert transform on the unit circle is considered. Its Moore--Penrose inverse with respect to suitable scalar products is derived for different side conditions. Furthermore, stability of the pseudo-inverse is studied. These results allow the efficient computation of approximate solutions of singular integral equations with Hilbert kernel. Furthermore, the stability analysis of such methods becomes much easier even for graded meshes which are useful for weakly singular solutions.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1998-02-01 | SIAM Journal on Numerical Analysis |