On uniqueness of series by general Franklin system (Q1616195)
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scientific article; zbMATH DE number 6969894
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On uniqueness of series by general Franklin system |
scientific article; zbMATH DE number 6969894 |
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On uniqueness of series by general Franklin system (English)
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1 November 2018
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This paper studies the general Franklin system of orthonormal piecewise linear functions associated to an arbitrary partition of \([0,1]\) that satisfies a certain regularity condition. The main result establishes the uniqueness and a recovery formula for the coefficients of multivariable Franklin series on the cube \([0,1]^d\), subject to the series' convergence in measure and to a technical assumption expressed in terms of the square-type partial sums.
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general Franklin system
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uniqueness theorem
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recovery formula
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\(A\)-integral
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