APPROXIMATION OF FUNCTION BY CONVOLUTION
This thesis discusses about approximation of functions by convolution. There are convolutors which are dilations of a kernel and those which are kernels without dilation. We discuss suficient conditions for the convolutors and examples of the convolutors. From existing results, we do not find many k...
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| Format: | Theses |
| Language: | Indonesia |
| Subjects: | |
| Online Access: | https://digilib.itb.ac.id/gdl/view/34771 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | This thesis discusses about approximation of functions by convolution. There are convolutors which are dilations of a kernel and those which are kernels without dilation. We discuss suficient conditions for the convolutors and examples of the convolutors. From existing results, we do not find many kernels without dilation as convolutors. A famous kernel without dilation, known as Landau kernel, which is used in the proof of Weierstrass Approximation theorem, has compact support. In this thesis, we will contruct a new kernel without dilation as a convolutor which has support in RS. We will also give an ilustration about its rate of convergence in approximating functions and examples of its application in image processing |
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