TY  - INPR
A1  - Kammann, Paula
A1  - Michel, Volker
T1  - Time-Dependent Cauchy-Navier Splines and their Application to Seismic Wave Front Propagation
N2  - In this paper a known orthonormal system of time- and space-dependent functions, that were derived out of the Cauchy-Navier equation for elastodynamic phenomena, is used to construct reproducing kernel Hilbert spaces. After choosing one of the spaces the corresponding kernel is used to define a function system that serves as a basis for a spline space. We show that under certain conditions there exists a unique interpolating or approximating, respectively, spline in this space with respect to given samples of an unknown function. The name "spline" here refers to its property of minimising a norm among all interpolating functions. Moreover, a convergence theorem and an error estimate relative to the point grid density are derived. As numerical example we investigate the propagation of seismic waves.
T3  - Schriften zur Funktionalanalysis und Geomathematik - 26 
KW  - Spline
KW  - Sphäre
KW  - Elastizität
KW  - Seismische Welle
KW  - Zeitabhängigkeit
KW  - Approximation
KW  - reproduzierender Kern
KW  - Cauchy-Navier-Gleichung
KW  - reproducing kernel
KW  - spline
KW  - sphere
KW  - seismic wave
KW  - Cauchy-Navier equation
Y1  - 2006
UR  - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1760
UR  - https://nbn-resolving.org/urn:nbn:de:hbz:386-kluedo-14373
ER  -