Kernel frame smoothing operators

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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.
Related projects:	Functional-differential equations and mathematical-statistical models