Publication details

Kernel frame smoothing operators

Authors

VESELÝ Vítězslav

Year of publication 2001
Type Article in Proceedings
Conference Proceedings ROBUST'2000
MU Faculty or unit

Faculty of Science

Citation
Field General mathematics
Keywords nctional approximation; kernel operators;frame and wavelet expansions; pseudoinverse operators
Description Basics of frame expansions in separable Hilbert spaces are explained in context with the theory of pseudoinverse operators. A new geometric approach is outlined connecting both areas. An iterative frame-based procedure is suggested which finds, to a given function, a finite frame or Riesz basis for its expansion which is suboptimal in a certain sense. In particular a new type of kernel smoothing operator based on dual frame expansions is introduced with which the above procedure allows us to find easily not only suboptimal bandwidths (scales) as with common kernel smoothing, but also suboptimal shifts.
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