Enhanced L1-Convergence Theorems for Modified Cosine and Sine Series
DOI:
https://doi.org/10.31305/rrijm2025.v05.n04.012Keywords:
Cosine Series, Sine Series, Trigonometric Sums, Convergence TheoremsAbstract
This paper builds on previous research that examined the L1-convergence of modified sine and cosine series. We demonstrate enhanced convergence theorems that expand and extend previous results in this domain by incorporating particular novel types of coefficients. The analysis employs summability techniques and revised inequalities to enhance the sufficient requirements for L1-convergence of trigonometric series. These results not only validate previously established theorems but also establish a foundation for a broader framework applicable to an expanded class of modified trigonometric sums. Our findings illuminate the dynamics of convergence in Fourier-type expansions and propose novel avenues for investigation in harmonic analysis and approximation theory.
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