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Norm equivalence between convolution operator in the discrete space (discrete analogue) and convolution in the continue space was given by Magyar, Stein, and Wainger in [3] focusing on Fourier transform. Hilbert transform was written sophisticately by King in [1]. This undergraduate thesis shows the...
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| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/17321 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Norm equivalence between convolution operator in the discrete space (discrete analogue) and convolution in the continue space was given by Magyar, Stein, and Wainger in [3] focusing on Fourier transform. Hilbert transform was written sophisticately by King in [1]. This undergraduate thesis shows the relation between [3] and [1] regarding Hilbert transform as a convolution. The …rst part gives some details for [3], the second part narrows down the way of …nding the Hilbert transform using the complex function approach, especially via Poisson Integral Formula, and <br />
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the last part investigates norm boundedness on the analog of the discrete Hilbert transform. Although there is nothing new, this undergraduate thesis gives the more <br />
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simple perspective on those matters for the easing of reading a book or paper for undergraduate students. |
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