We prove norm inequalities with exponential weights for the Riemann Liouville fractional integral. As an application, we show for certain functions that their Laguerre expansions will converge in the L p norm for some p outside the standard range of (4Γ3, 4).
An application of fractional integration to a long temperature series
β Scribed by L. A. Gil-Alana
- Publisher
- John Wiley and Sons
- Year
- 2003
- Tongue
- English
- Weight
- 153 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0899-8418
- DOI
- 10.1002/joc.968
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β¦ Synopsis
Abstract
Some recently proposed techniques of fractional integration are applied to a long UK temperature series. The tests are valid under general forms of serial correlation and do not require estimation of the fractional differencing parameter. The results show that central England temperatures have increased about 0.23 Β°C per 100 years in recent history. Attempting to summarize the conclusions for each of the months, we are left with the impression that the highest increase has occurred during the months from October to March. Copyright Β© 2003 Royal Meteorological Society
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