On some properties of fractional dyadic derivative and integral

On some properties of fractional dyadic derivative and integral

For the fractional dyadic derivative and integral, the following analogues of two theorems of Lebesgue are proved: the theorem on differentiation of the indefinite Lebesgue integral of an integrable function at its Lebesgue points, and the theorem on reconstruction of an absolutely continuous functi...

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Bibliographic Details
Published in:Analysis mathematica (Budapest) Vol. 32; no. 3; pp. 173 - 205
Main Author: Golubov, Boris I.
Format: Journal Article
Language:English
Published: 01-09-2006
Subjects:
Derivatives
Differentiation
Dyadics
Integrals
Mathematical analysis
Reconstruction
Theorems
Online Access:Get full text
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Summary:For the fractional dyadic derivative and integral, the following analogues of two theorems of Lebesgue are proved: the theorem on differentiation of the indefinite Lebesgue integral of an integrable function at its Lebesgue points, and the theorem on reconstruction of an absolutely continuous function by means of its derivative. Dyadic fractional analogues of the formula of integration by parts are also obtained. In addition, some theorems are proved on dyadic fractional differentiation and integration of a Lebesgue integral depending on a parameter. Most of the results are new even for dyadic derivatives and integrals of natural order.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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content type line 23
ISSN:0133-3852
1588-273X
DOI:10.1007/s10476-006-0010-0