THE BOUNDEDNESS OF BAND-LIMITEDWAVELET DECOMPOSITION OPERATOR IN MORREY SPACE
The study of function spaces such as Lebesgue and Morrey spaces is motivated by the need to solve partial differential equations that are apparent in many problems such as physical phenomena. To examine such functions, a decomposition which breaks down those functions into several simpler functio...
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| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/54999 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | The study of function spaces such as Lebesgue and Morrey spaces is motivated by
the need to solve partial differential equations that are apparent in many problems
such as physical phenomena. To examine such functions, a decomposition which
breaks down those functions into several simpler functions is needed. One of those
simpler functions are wavelets. Wavelets are functions descended from a single
mother function which is modified only by translation and dilation. This research
primarily concerns wavelets which are orthonormal and band-limited. One method
to decompose Lebesgue and Morrey functions is through the use of a waveletrelated
operator called the W! operator, where the ! is the mother function. In
this study, we described a norm equivalency between Lebesgue functions and their
mapped functions through the W! operator. Afterwards, we tried to extend this
result into Morrey spaces and obtained the boundedness of this operator or a halfequivalency. |
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